Minimizing the Cost of a Box
Finding the minimum cost of a box given the volume and cost of materials
tags:
Cost Function Critical Value Derivative Domain How-To Calculus Optimization Price-Demand Function Profit Function Revenue FunctionFinding the Price to Maximize Profit
Author: ShaNisaa RaSun
The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Answer" to reveal the answer to the problem.
Problem: A company that makes toy firetrucks has a price-demand function given by \(p(x)=-0.02x+45,\) where \(x\) is the number of trucks sold at a price of \(\$p\) each. The company has a weekly cost function, in dollars, given by \(C(x)=12x+1000,\) where \(x\) is the number of trucks manufactured each week. Determine the selling price of each truck that will maximize the company's profit.
The selling price of each truck that will maximize the company's profit is \(\$28.50.\)
See more videos from this section
Related Videos
Solving a Related Rates Word Problem About Profit
Finding the rate of change of profit given the rate of increase for sales
Increasing and Decreasing and Local Extrema for a Revenue Function
Finding intervals of increase/decrease and the local extema for revenue from a word problem
Finding the Box with the Largest Volume
Finding the dimensions of the box with the largest volume given the amount of material to make the box
Calculating Marginal Revenue
Finding the marginal revenue given the price-demand function for a word problem
Increasing and Decreasing and Local Extrema
Finding the intervals where a function is increasing/decreasing and the local extrema
Absolute Extrema on a Closed Interval
Finding the absolute maximum and minimum of a rational function on two closed intervals
Absolute Extrema on a Closed Interval 2
Finding the absolute maximum and absolute minimum of a rational function on two closed intervals
Maximizing a Product of Numbers
Finding the maximum product of two numbers given their sum is 100
MATH 140 2.2 Exercise 2
Finding linear functions for the cost, revenue, and profit of a business
MATH 140 2.2 Exercise 5
Finding the linear profit function for a company
MATH 140 Exam 1 Review #4
Finding the break-even point for a company given the profit function
MATH 140 Exam 1 Review #19
Finding the cost, revenue, and profit equations for a given problem
MATH 140 5.2 Exercise 8
Finding the maximum revenue, maximum profit, and break even quantity for given revenue and cost functions
Finding Critical Values
Finding the critical values for several functions
Inflection Points and Intervals of Concavity for an Exponential Function
Finding the intervals of concavity and inflection points for a function with exponentials
Inflection Points and Intervals of Concavity from a Graph
Determining the intervals of concavity and inflection points from the graph of a function
Using the Second Derivative Test to Find Local Extrema
Using the second derivative test to find local extrema for a function
Studying the Shape of Curves: MATH 151 4.1 Problems 2-7
Using derivatives to find properties of graphs
Studying the Shape of Curves: MATH 151 Problems 2-7
Using derivatives to find properties of graphs
Studying the Shape of Curves: MATH 151 4.1 Problems 2-7
Using derivatives to find properties of graphs
Studying the Shape of Curves: MATH 151 Problems 2-7
Using derivatives to find properties of graphs
Instantaneous Rate of Change of Profit
Finding the instantaneous rate of change of profit for a given price-demand function and cost function
Determining Where the Derivative Exists From a Graph
Determining where the derivative of a function does not exist from a graph
Finding a Derivative with Exponential Functions and Logarithms
Finding the derivative a function with a power, exponential, and logarithm
Finding a Derivative by Simplifying a Rational
Finding the derivative of a rational function by simplifying and using the power rule
Evaluating Derivatives From a Given Table
Finding and evaluating derivatives using values given in a table
Using the Product Rule with a Logarithm
Finding a derivative of a function with a logarithm using the Product Rule
Using the Product Rule with an Exponential
Finding the derivative of a function with a square root and exponential using the Product Rule
The Quotient Rule with an Exponential
Finding the derivative of a fraction with an exponential using the Quotient Rule
Using Both the Quotient and Product Rule
Finding a derivative using both the Product and Quotient Rule
Using the Product and Quotient Rules with a Table
Finding a derivative using the Product and Quotient Rule and values given in a table
Finding Marginal Cost and Marginal Average Cost
Finding the derivative of both the cost function and average cost function
Using Log Properties to Simplify Before Taking the Derivative
Using logarithm properties to simplify before using the Chain Rule to find a derivative
Using Log Properties to Simplify Before Taking the Derivative 2
Using logarithm properties to simplify before using the Generalized Logarithm Rule to find a derivative
Using the Chain Rule with a Table
Using the chain rule to find derivates with some values given in a table
Calculating the Rate of Growth With Compound Interest
Finding the rate a balance is increasing for interest compounded monthly and continuously
Using the Alternate Form of the Chain Rule
Using the alternate form of the Chain Rule to find the derivative
Using Logarithmic Differentiation to Find a Derivative
Finding the derivative of a function that requires logarithmic differentiation
Using the Generalized Power Rule
Finding the derivative of a function using the Generalized Power Rule
Solving a Related Rates Word Problem About a Sliding Ladder
Finding how fast a ladder moves up a wall as the bottom is being pushed
Using Implicit Differentiation to Find a Derivative
Using implicit differentiation to find the derivative of a function
Using Implicit Differentiation to Find a Derivative 2
Using implicit differentiation to find the derivative of a function
Solving a Related Rates Word Problem About Liquid Filling a Sphere
Finding the rate water is flowing into an expandable sphere given the rate a sphere is growing
Using the Quotient Rule Twice to Find the Second Derivative
Using the quotient rule twice to find the second derivative of a rational function
Finding a Function from its Derivative and One Value
Solving for a function given its derivate and one value
Finding the Cost Function from Marginal Cost
Solving the antiderivative of marginal cost to find the cost function and evaluating a particular cost
Finding the Function from Its Derivative Using u-Substitution
Using u-substitution in an indefinite integral to find a function from its derivative and a given vaue
Calculating Profit From Marginal Profit Using u-Substitution
Calculating profit from marginal profit using an indefinite integral and u-substitution
Optimization Example 1
Solving an optimization word problem using a derivative
Optimization Example 2
Using the second derivative to find the maximum rate of change in a word problem
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions
Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19
Mean Value Theorem and using derivatives to find the shape of curves
Inverse Trigonometric Functions: MATH 151 1.5 Problems 9-12
Properties and derivatives of inverse trigonometric functions
Inverse Trigonometric Functions: MATH 151 Problems 9-12
Properties and derivatives of inverse trigonometric functions
MLC WIR 20B M151 week7 #1a
Finding the absolute maximum and absolute minimum values of a function on a closed interval
MLC WIR 20B M151 week7 #1b
Finding the absolute maximum and absolute minimum values of a function on a closed interval
MLC WIR 20B M151 week7 #1c
Finding the absolute maximum and absolute minimum values of a function on a closed interval
MLC WIR 20B M151 week7 #3
Sketching a curve given information about the function and its derivatives
MLC WIR 20B M151 week7 #5
Using the first and second derivatives to sketch the graph of a function
MLC WIR 20B M151 week8 #1
Solving a word problem minimizing area
MLC WIR 20B M151 week8 #2
Solving a word problem maximizing area
MLC WIR 20B M151 week8 #3
Finding the point on a line closest to a point
MLC WIR 20B M151 week9 #2
Using the derivative to determine where a function is increasing and decreasing
MLC WIR 20B M151 week9 #3
Finding the absolute maximum and minimum values of a function on a closed interval
MLC WIR 20B M151 week9 #4
Finding the intervals where a function is increasing and decreasing and its local maximums and minimums
MLC WIR 20B M151 week9 #5
Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points
MLC WIR 20B M151 week9 #6
Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points
MLC WIR 20B M151 week9 #7
Finding where a function is increasing, decreasing, concave up and concave down and its local extrema and inflection points
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions
Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19
Mean Value Theorem and using derivatives to find the shape of curves
Inverse Trigonometric Functions: MATH 151 1.5 Problems 9-12
Properties and derivatives of inverse trigonometric functions
Inverse Trigonometric Functions: MATH 171 Problems 4-6
Properties of inverse trig functions and the derivative of arctangent
Inverse Trigonometric Functions: MATH 151 Problems 9-12
Properties and derivatives of inverse trigonometric functions
Absolute Extrema: MATH 171 Problems 4 & 5
Proving Fermat's Theorem and graphing local and absolute extrema
Optimization: MATH 171 Problems 1-3
Optimizing values in word problems
Math 140 Exam 3 Review Exercise 8
Finding the maximum profit for a word problem given the cost and price-demand equation
Finding Intervals of Increase/Decrease and Concavity in Python
Using Python to find the intervals where a function is increasing or decreasing
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions
MATH 140 2.2 Exercise 3
Finding the linear cost function for a company
MATH 140 2.2 Exercise 4
Finding the linear revenue function for a company
MATH 140 3.3 Exercise 1
Maximizing profit subject to a set of constraints
MATH 140 3.3 Exercise 2
Maximizing wages subject to a set of constraints
MATH 140 3.4 Exercise 6
Interpreting a final tableau of the simplex method for a word problem
MATH 140 5.1 Exercise 2
Determining the domain and range of a relation and if the relation is a function
MATH 140 5.1 Exercise 3
Determining the domain and range of a relation and if the relation is a function
MATH 140 5.1 Exercise 4
Determining the domain and range of a relation and if the relation is a function
MATH 140 5.2 Exercise 2
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.2 Exercise 3
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.2 Exercise 4
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.2 Exercise 5
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.2 Exercise 6
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
MATH 140 5.5 Exercise 1
Finding the domain of a piecewise function and evaluating it
MATH 140 5.5 Exercise 2
Finding the piecewise-defined function for a given graph along with its domain and range
MATH 140 5.6 Exercise 1
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
MATH 140 5.6 Exercise 2
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
MATH 140 5.6 Exercise 3
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
MATH 140 5.6 Exercise 4
Finding the domain of a function that is a fraction containing an exponential and root
MATH 140 5.6 Exercise 5
Finding the domain of a function that is a fraction containing an exponential and root
MATH 140 5.6 Exercise 6
Finding the domain of a function that is a fraction containing exponentials and a square root
MATH 140 5.8 Exercise 7
Finding the domain, range, end behavior, and intercepts for a logarithmic function
MATH 140 5.8 Exercise 9
Finding the domain of a function containing a logarithm, exponential, radical, and fraction
MATH 140 5.8 Exercise 10
Finding the domain of a function containing several logarithms
MATH 140 5.8 Exercise 11
Finding the domain of a function containing a logarithm, exponential, and fraction
MATH 140 5.3 Exercise 1
Finding the domain, intercepts, asymptotes, and holes of a rational function
MATH 140 5.3 Exercise 2
Finding the domain, intercepts, asymptotes, and holes of a rational function
MATH 140 5.3 Exercise 3
Finding the domain, intercepts, asymptotes, and holes of a rational function
Evaluating Limits from a Graph
Finding limits from the graph of a piecewise function
Evaluating One-Sided Limits from a Graph
Finding one-sided limits from the graph of a piecewise function
Evaluating a Limit Numerically
Finding the limit of a function numerically using a calculator
Combinations of Limits from Graphs
Finding limits of combinations of functions using their graphs
Evaluating Limits Algebraically
Using the properties of limits to find several limits algebraically
Limit of a Piecewise Function
Finding one and two-sided limits for a piecewise function algebraically
Limit of a Rational Function
Finding the limit of a rational function algebraically
Limit of a Rational Function 2
Finding the limit of a rational function algebraically
Limit with Multiple Fractions
Finding the limit algebraically of a function with multiple fractions
Limit of a Fraction with a Square Root
Finding the limit algebraically of a function with a square root in the numerator of a fraction
Limit with an Absolute Value
Finding the limit algebraically of a function with an absolute value
Limit at Negative Infinity of a Rational Function
Solving a limit approaching negative infinity for a rational function
Limits at Infinity of a Rational Function
Solving the limits approaching infinity and negative infinity of a rational function
Limits at Infinity of a Rational Function 2
Solving the limits approaching infinity and negative infinity of a rational function
Limits at Infinity of a Fraction with Exponential Functions
Solving the limits approaching infinity and negative infinity with exponential functions in the numerator and denominator
Vertical Asymptotes and Holes of a Rational Function
Finding the holes and vertical asymptotes of a rational function
Horizontal Asymptote of a Fraction with Exponential Functions
Finding the horizontal asymptotes of a function that is a fraction with exponentials in the numerator and denominator
Where the Graph of a Function is Not Continuous
Determining where a piecewise function is continuous from its graph
Continuity of a Function with a Cube Root
Finding where a function with a fraction and cube root is continuous
Continuity of a Function with a Square Root and Logarithm
Determining where a function with a fraction, square root, and logarithm is continuous
Continuity of a Piecewise Function
Determining where a piecewise function is continuous algebraically
Solving for a Constant so a Piecewise Function is Continuous
Solving for a constant to make a piecewise-defined function continuous for all real numbers
Average Rate of Change from a Table
Finding the average rate of change over time periods from a table
Slope of a Secant Line
Finding the slope of a secant line to a given function
Instantaneous Rate of Change of a Function
Finding the exact value of the instantaneous rate of change
Instantaneous Rate of Change of a Rational Function
Finding the exact value of the instantaneous rate of change
Slope of a Tangent Line
Finding the equation of the tangent line to a function using the limit definition
Finding the Derivative of a Polynomial Using the Limit Definition
Using the limit definition to find the derivative of a polynomial
Finding the Derivative of a Rational Function Using the Limit Definition
Using the limit definition to find the derivative of a rational function
Finding the Derivative of a Root Function Using the Limit Definition
Using the limit definition to find the derivative of a square root function
Using the Quotient Rule on a Rational Function
Finding the derivative of a rational function using the Quotient Rule
Using the Generalized Exponential Rule
Using the Generalized Exponential Rule to find the derivative of a function
Finding Where a Function is Increasing and Decreasing
Determining the intervals where a function is increasing and decreasing
Local and Absolute Extrema from a Graph
Finding all local and absolute extrema of a function from a graph
Finding an Antiderivative
Finding the antiderivative of a function
Finding an Indefinite Integral
Evaluating an indefinite integral with an exponential
Finding an Indefinite Integral with a Fraction
Solving an indefinite integral by first simplifying the fraction
u-Substitution With an Exponential Function
Solving an indefinite integral with an exponential function suing u-substitution
u-Substitution With a Natural Logarithm
Solving an indefinite integral with a natural logarithm using u-substitution
u-Substitution With a Quotient and Exponentials
Solving an indefinite integral with exponentials in a quotient using u-substitution
u-Substitution With a Quotient and a Root
Solving an indefinite integral with a cube root in the denominator using u-substitution
Calculating the Exact Area Under a Curve With Geometry
Using geometric formulas for circles, triangles, and rectangles to find the exact area under a curve
Introduction to Riemann Sums
Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums
Estimating Area With a Right-Hand Riemann Sum
Estimating the area under a curve using right-hand Riemann sums
Estimating Area With a Left-Hand Riemann Sum
Estimating the area under a curve using left-hand Riemann sums
Estimating Area With a Midpoint Riemann Sum
Estimating the area under a curve using midpoint Riemann sums
Estimating the Area Under a Curve With a Riemann Sum
Estimating the area under a graph using right-hand Riemann sums
Calculating a Definite Integral From a Graph
Calculating a definite integral by finding the area under a curve using geometry
Definite Integral Comparison Properties
Comparing two definite integrals with the same limits of integration
Evaluating a Definite Integral
Using the Fundamental Theorem of Calculus to evaluate a definite integral
Evaluating a Definite Integral 2
Using the Fundamental Theorem of Calculus to evaluate a definite integral
Evaluating a Definite Integral with u-Substitution
Using the Fundamental Theorem of Calculus and \(u\)-substitution to evaluate a definite integral
Part 1 of the Fundamental Theorem of Calculus
Using Part 1 of the Fundamental Theorem of Calculus to find the derivative of a function defined using an integral
Solving a Word Problem With a Definite Integral
Solving a word problem using a definite integral and the Fundamental Theorem of Calculus
Average Value of a Function
Finding the average value of a a function on an interval using a definite integral
Area Between Two Curves
Finding the area between two curves on an interval using a definite integral
Area of the Region Bounded by Two Curves
Finding the area of a region bounded by two curves using definite integrals
Related Rates Example 1
Solving a related rates word problem for the rate of change of a cell's radius
Related Rates Example 2
Solving a related rates word problem on blood flow and the Poiseuille equation
Higher Derivatives Example 1
The definition of higher derivatives and solving an example
Higher Derivatives Example 2
Using derivatives to find the velocity and acceleration functions from the position function
Derivatives of Exponential Functions
Explaining the formulas for the derivatives of exponential functions
Derivatives of Exponential Functions Example 1
Calculating the derivative of a function with exponentials using the chain and product rule
Derivatives of Exponential Functions Example 2
Calculating a derivative of a quotient with an exponential function
Linear Approximation Example
Using a linear approximation and the per capita growth rate to estimate population size
WIR2 20B M150 V10
Finding the domains of functions
WIR8 20B M150 V03
Finding the domains of expressions
WIR3 20B M150 V13
Determining the properties of a rational function and graphing it
WIR8 20B M150 V09
Determining the properties of a rational function and graphing it
WIR3 20B M150 V20
Restricting the domain of a function so it is one-to-one and has an inverse
WIR3 20B M150 V21
Determining algebraically the inverse of a function
WIR3 20B M150 V22
Determining algebraically the inverse of a function
WIR3 20B M150 V23
Determining algebraically the inverse of a function
WIR4 20B M150 V1
Determining properties of an exponential function
WIR4 20B M150 V2
Determining properties of an exponential function
WIR4 20B M150 V3
Determining properties of an exponential function
WIR4 20B M150 V4
Identifying the graph of an exponential function
WIR8 20B M150 V10
Determining properties of an exponential function
WIR4 20B M150 V7
Determining the properties of a logarithmic function
WIR4 20B M150 V8
Determining the graph of a logarithmic function
WIR4 20B M150 V9
Determining the properties of a logarithmic function
WIR4 20B M150 V10
Determining the graph of a logarithmic function
WIR4 20B M150 V19
Solving an equation with an exponential function
WIR4 20B M150 V20
Solving an equation with exponential functions by factoring
WIR2 20B M150 V11
Using a graph to evaluate a function
Parametric Curves: MATH 151 J.3 Problems 1-5
Cartesian equations and parametric equations of curves
Vectors and Derivatives: MATH 151 K.1 Problems 1-8
Derivatives and vectors with some physics applications
Derivatives and Applications: MATH 151 K.2 Problems 9-15
Tangent lines to parametric equations and related rates examples
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for the Common Exam: MATH 151 Exam 2 Review Problems 10-15
Implicit differentiation and physics applications of derivatives
Review for the Common Exam: MATH 151 Exam 2 Review Problems 16-20
Derivatives of parametric equations and tangent lines
Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7
Derivatives of exponential functions and the exponential model
Review for the Common Exam: MATH 151 Exam 2 Review Problems 1-9
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29
Related rates problems, differentials, linear and quadratic approximations
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for Common Exam: MATH 151 Exam 3 Review Problems 22-24
Optimization problems
Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30
Antiderivatives and physics applications
Continuity: MATH 151 2.5 Problems 1-6
Continuity of Functions and the Intermediate Value Theorem
Approximations and Exponentials: MATH 151 2.6 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Differentials and Approximations: MATH 151 3.10 Problems 1-6
Differentials, linear approximations and quadratic approximations
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Trigonometry Derivatives and the Chain Rule: MATH 151 3.3 Problems 1-9
Derivatives of trigonometric functions and using the Chain Rule
Approximations and Exponentials: MATH 151 3.4 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Trigonometry Derivatives and the Chain Rule: MATH 151 3.4 Problems 1-9
Derivatives of trigonometric functions and using the Chain Rule
Vectors and Derivatives: MATH 151 3.4 Problems 1-8
Derivatives and vectors with some physics applications
Implicit Differentiation: MATH 151 3.5 Problems 10-13
Implicit differentiation and finding tangent lines
Differentiation and Applications: MATH 151 Problems 1-8
Derivatives of exponential and logarithmic functions and the exponential model
Vectors and Derivatives: MATH 151 3.7 Problems 1-8
Derivatives and vectors with some physics applications
Differentiation and Applications: MATH 151 3.8 Problems 1-8
Derivatives of exponential and logarithmic functions and the exponential model
Derivatives and Applications: MATH 151 3.9 Problems 9-15
Tangent lines to parametric equations and related rates examples
Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.2 Problems 1-6
Mean Value Theorem and properties of a graph
Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.3 Problems 1-6
Mean Value Theorem and properties of a graph
Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12
Using Reimann sums and the Fundamental Theorem of Calculus
Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12
Using Riemann sums and the Fundamental Theorem of Calculus
MLC WIR 20B M151 week3 #17
Using the graph of a function to sketch a graph of its derivative
MLC WIR 20B M151 week3 #21
Finding the derivative of a function using the limit definition
MLC WIR 20B M151 week3 #22
Finding the derivative of a function using the limit definition
MLC WIR 20B M151 week3 #23
Finding the derivative of a function using the limit definition
MLC WIR 20B M151 week4 #1ab
Differentiating functions using the Power Rule
MLC WIR 20B M151 week4 #1cd
Differentiating a function using the Power Rule
MLC WIR 20B M151 week4 #1e
Differentiating a function with an exponential function and using the Power Rule
MLC WIR 20B M151 week4 #1f
Using the Product Rule to differentiate a function
MLC WIR 20B M151 week4 #1g
Using the Quotient Rule to differentiate a function
MLC WIR 20B M151 week4 #1h
Using the Quotient Rule to differentiate a rational function
MLC WIR 20B M151 week4 #1i
Using the Product Rule to differentiate a function
MLC WIR 20B M151 week4 #1j
Using the Product and Quotient Rules to differentiate a function
MLC WIR 20B M151 week4 #2a
Using the Product Rule to find a first and second derivative
MLC WIR 20B M151 week4 #1kl
Using the Chain Rule to differentiate functions
MLC WIR 20B M151 week4 #1mn
Using the Chain Rule to differentiate functions with exponential and trigonometric functions
MLC WIR 20B M151 week4 #1o
Using the Chain Rule to differentiate a function containing trigonometric functions
MLC WIR 20B M151 week4 #2b
Using the Chain Rule to find a first and second derivative
MLC WIR 20B M151 week4 #3
Using the Chain Rule to evaluate the derivative of a composition of functions
MLC WIR 20B M151 week4 #4
Using the Chain Rule to evaluate the derivative of a composition of functions
MLC WIR 20B M151 week4 #5
Using the Chain Rule to find the pattern for a higher order derivative
MLC WIR 20B M151 week4 #6
Using the Chain Rule to find the pattern for a higher order derivative
MLC WIR 20B M151 week4 #7
Finding the derivatives of compositions of functions from their graphs
MLC WIR 20B M151 week5 #1a
Finding the derivative using implicit differentiation
MLC WIR 20B M151 week5 #1b
Finding the derivative using implicit differentiation
MLC WIR 20B M151 week5 #1c
Finding the derivative using implicit differentiation
MLC WIR 20B M151 week5 #1d
Finding the derivative using implicit differentiation
MLC WIR 20B M151 week5 #2
Finding the derivative using implicit differentiation
MLC WIR 20B M151 week5 #3a
Finding a tangent line to an curve defined implicitly
MLC WIR 20B M151 week5 #3b
Finding a tangent line to an curve defined implicitly
MLC WIR 20B M151 week5 #4ab
Finding the derivative of a function containing an inverse trigonometric function
MLC WIR 20B M151 week5 #4cd
Finding the derivative of a function containing an inverse trigonometric function
MLC WIR 20B M151 week5 #4ef
Finding the derivative of a function containing a logarithmic function
MLC WIR 20B M151 week5 #4ghi
Finding the derivatives of functions containing logarithms
MLC WIR 20B M151 week5 #5
Finding the derivative of a function containing a logarithms
MLC WIR 20B M151 week5 #6
Finding the equation of a tangent line to a function containing a logarithm
MLC WIR 20B M151 week5 #7a
Using logarithmic differentiation to find the derivative of a function
MLC WIR 20B M151 week5 #7b
Using logarithmic differentiation to find the derivative of a function
MLC WIR 20B M151 week5 #7c
Using logarithmic differentiation to find the derivative of a function
MLC WIR 20B M151 week5 #10
Finding the points on a parametric curve where the tangent line is horizontal or vertical
MLC WIR 20B M151 week5 #9a
Finding the tangent line to a parametric curve
MLC WIR 20B M151 week5 #9b
Finding the tangent line to a parametric curve
MLC WIR 20B M151 week6 #1ab
Using the Product and Chain Rule to find several derivatives
MLC WIR 20B M151 week6 #1cd
Using the Product, Quotient and Chain Rules to find several derivatives
MLC WIR 20B M151 week6 #1ef
Using the Quotient and Chain Rules to find several derivatives
MLC WIR 20B M151 week6 #1gh
Using the Product and Chain Rules to differentiate functions with logarithms
MLC WIR 20B M151 week6 #1ij
Differentiating functions with logarithmic and inverse trigonometric functions
MLC WIR 20B M151 week6 #1kl
Differentiating functions with inverse trigonometric functions
MLC WIR 20B M151 week6 #2a
Finding the derivative of an implicit function
MLC WIR 20B M151 week6 #2b
Finding the derivative of an implicit function
MLC WIR 20B M151 week6 #3
Using the chain rule to find a derivative
MLC WIR 20B M151 week6 #4a
Using logarithmic differentiation to find the derivative of a function
MLC WIR 20B M151 week6 #4b
Using logarithmic differentiation to find the derivative of a function
MLC WIR 20B M151 week6 #5a
Using the Product Rule to find the derivative of a product of functions
MLC WIR 20B M151 week6 #5b
Using the Quotient Rule to find a derivative
MLC WIR 20B M151 week6 #5c
Using the Chain Rule to find the derivative of a composition of functions
MLC WIR 20B M151 week6 #6
Finding the second derivative of an exponential functino
MLC WIR 20B M151 week6 #7
Finding the speed of an object given a vector function for its position
MLC WIR 20B M151 week6 #8
Finding the point when the tangent line to a function has a particular slope
MLC WIR 20B M151 week6 #9
Finding where a function has horizontal tangent lines
MLC WIR 20B M151 week6 #10
Finding a higher order derivative of a function
MLC WIR 20B M151 week6 #12
Using the derivative to find the total distance traveled by a particle
MLC WIR 20B M151 week6 #13
Finding where the tangent line is horizontal or vertical for a parametric equation
MLC WIR 20B M151 week6 #14
Finding the equation of a tangent line to a parametric curve
MLC WIR 20B M151 week6 #15
Finding the equation of a tangent line to an implicit function
MLC WIR 20B M151 week6 #16
Solving for constants so that a piecewise function is differentiable everywhere
MLC WIR 20B M151 week6 #17
Finding the linear approximation for a function
MLC WIR 20B M151 week6 #11
Using a linear approximation to approximate the value of a function
MLC WIR 20B M151 week7 #2a
Finding a number that satisfies the conclusion of the Mean Value Theorem on an interval
MLC WIR 20B M151 week7 #2b
Finding a number that satisfies the conclusion of the Mean Value Theorem on an interval
MLC WIR 20B M151 week7 #4a
Evaluating a limit using L'Hospital's Rule
MLC WIR 20B M151 week7 #4b
Evaluating a limit using L'Hospital's Rule
MLC WIR 20B M151 week7 #4c
Evaluating a limit using L'Hospital's Rule
MLC WIR 20B M151 week7 #4d
Evaluating a limit using L'Hospital's Rule
MLC WIR 20B M151 week7 #4e
Evaluating a limit with an indeterminate product using L'Hospital's Rule
MLC WIR 20B M151 week7 #4f
Evaluating a limit with an indeterminant difference using L'Hospital's Rule
MLC WIR 20B M151 week7 #4g
Evaluating a limit with an indeterminate power using L'Hospital's Rule
MLC WIR 20B M151 week7 #4h
Evaluating a limit with an indeterminant power using L'Hospital's Rule
MLC WIR 20B M151 week9 #1
Determining the properties of a function from the graph of its derivative
MLC WIR 20B M151 week9 #8c
Evaluating a limit using L'Hospital's Rule
MLC WIR 20B M151 week9 #8d
Evaluating a limit with an indeterminant power using L'Hospital's Rule
MLC WIR 20B M151 week9 #8e
Evaluating a limit with an indeterminant product using L'Hospital's Rule
MLC WIR 20B M151 week9 #9
Finding a number that satisfies the conclusion of the Mean Value Theorem for a function on an interval
MLC WIR 20B M151 week9 #8f
Evaluating a limit with an indeterminant product using L'Hospital's Rule
MLC WIR 20B M151 week9 #10a
Finding the antiderivative of a polynomial
MLC WIR 20B M151 week9 #10b
Finding the antiderivative of a rational function
MLC WIR 20B M151 week9 #10c
Finding the antiderivative of a function with secant and tangent
MLC WIR 20B M151 week9 #10d
Finding the antiderivative of a function and using a function value to find the constant
MLC WIR 20B M151 week9 #10e
Antidifferentiating twice to find a function from its second d
MLC WIR 20B M151 week9 #10f
Antidifferentiating twice to find a function from its second d
MLC WIR 20B M151 week10 #6c
Using L'Hospital's Rule to evaluate a limit representing a derivative at a point
MLC WIR 20B M151 week10 #9a
Finding a derivative using the Product Rule
MLC WIR 20B M151 week10 #9b
Finding a derivative using the Chain Rule multiple times
MLC WIR 20B M151 week10 #9c
Finding a derivative using the Chain Rule and Product Rule
MLC WIR 20B M151 week10 #9d
Finding a derivative using the Quotient Rule
MLC WIR 20B M151 week10 #10a
Finding the derivative of an implicit function
MLC WIR 20B M151 week10 #10b
Finding the derivative of an implicit function
MLC WIR 20B M151 week10 #11
Using logarithmic differentiation to find the derivative of a function
MLC WIR 20B M151 week10 #12
Finding the tangent line to a parametric curve
MLC WIR 20B M151 week10 #13
Finding when the tangent line to a parametric curve is vertical or horizontal
MLC WIR 20B M151 week10 #15
Determining the rate that the area of a triangle is increasing based on the rate an angle is increasing
MLC WIR 20B M151 week10 #16
Using a linear approximation to estimate the value of a function
MLC WIR 20B M151 week10 #17
Finding the value for a function that satisfies the Mean Value Theorem on an interval
MLC WIR 20B M151 week10 #18
Determining the properties of a function from the graph of its derivative
MLC WIR 20B M151 week10 #19a
Using L'Hospital's Rule to solve a limit
MLC WIR 20B M151 week10 #19b
Using L'Hospital's Rule to solve a limit with an indeterminant product
MLC WIR 20B M151 week10 #19c
Using L'Hospital's Rule to solve a limit with an indeterminant difference
MLC WIR 20B M151 week10 #19d
Using L'Hospital's Rule to solve a limit with an indeterminant power
WIR 20B M152 V88
Finding the length of a curve given by parametric equations
WIR 20B M152 V90
Finding the surface area of a rotated parametric curve
WIR 20B M152 V81
Finding the Taylor series of a function
WIR 20B M152 V82
Finding the Taylor series of a function
WIR 20B M152 V70
Determining if a series is absolutely convergent, conditionally convergent, or divergent.
WIR 20B M152 V76
Finding a power series representation for a function
Parametric Curves: MATH 151 J.3 Problems 1-5
Cartesian equations and parametric equations of curves
Vectors and Derivatives: MATH 151 K.1 Problems 1-8
Derivatives and vectors with some physics applications
Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3
Proving facts about the derivatives of vector functions including the product rule
Derivatives and Applications: MATH 171 Problems 7 & 8
Calculating slopes of tangent lines to parametric curves
Derivatives and Applications: MATH 151 K.2 Problems 9-15
Tangent lines to parametric equations and related rates examples
Review for the Common Exam: MATH 151 Exam 2 Review Problems 10-15
Implicit differentiation and physics applications of derivatives
Review for the Common Exam: MATH 151 Exam 2 Review Problems 16-20
Derivatives of parametric equations and tangent lines
Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7
Derivatives of exponential functions and the exponential model
Review for the Common Exam: MATH 151 Exam 2 Review Problems 1-9
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Review for the Common Exam: MATH 151 Exam 2 Review Problems 21-29
Related rates problems, differentials, linear and quadratic approximations
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for Common Exam: MATH 151 Exam 3 Review Problems 22-24
Optimization problems
Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30
Antiderivatives and physics applications
Continuity: MATH 151 2.5 Problems 1-6
Continuity of Functions and the Intermediate Value Theorem
Approximations and Exponentials: MATH 151 2.6 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Derivatives and Rates of Change: MATH 171 Problems 1-3
Using the limit definition to find derivatives of functions and vector functions
Differentiation Formulas: MATH 171 Problems 4 & 5
Using the limit definition to find a derivative and proving the power rule
Differentiation Formulas: MATH 171 Problems 6 & 7
Proving the Product Rule and the rule for the derivative of a difference of functions
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Differentials and Approximations: MATH 151 3.10 Problems 1-6
Differentials, linear approximations and quadratic approximations
Differentials: MATH 171 Problems 1 & 2
Proving facts about differentials including a product rule
Higher Order Derivatives: MATH 171 Problems 4-6
Finding a formula for a higher order derivative and a formula for the second derivative of a product
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Trigonometry Derivatives and the Chain Rule: MATH 151 3.3 Problems 1-9
Derivatives of trigonometric functions and using the Chain Rule
Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 1-3
Proving the derivatives of trigonometric functions and that sine is continuous
Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 4 & 5
Using the Chain Rule to prove facts about derivatives
Exponentials and Hyperbolic Trigonometric Functions: MATH 171 Problems 3 & 4
Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine
Approximations and Exponentials: MATH 151 3.4 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Trigonometry Derivatives and the Chain Rule: MATH 151 3.4 Problems 1-9
Derivatives of trigonometric functions and using the Chain Rule
Vectors and Derivatives: MATH 151 3.4 Problems 1-8
Derivatives and vectors with some physics applications
Implicit Differentiation: MATH 151 3.5 Problems 10-13
Implicit differentiation and finding tangent lines
Implicit Differentiation: MATH 171 Problems 6 & 7
Using implicit differentiation to solve a problem and to prove the power rule for rational exponents
Derivatives of Logarithmic Functions: MATH 171 Problems 1-3
Proving the derivative of ln(x) and the power and product rules using logarithmic differentiation
Differentiation and Applications: MATH 151 Problems 1-8
Derivatives of exponential and logarithmic functions and the exponential model
Derivatives and Applications: MATH 151 3.9 Problems 9-15
Tangent lines to parametric equations and related rates examples
Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.2 Problems 1-6
Mean Value Theorem and properties of a graph
Mean Value Theorem: MATH 171 Problems 6-8
Using the Mean Value Theorem to prove facts about functions
Studying the Shape of Curves: MATH 171 Problems 1-3
What the derivatives of a function tell us about the shape of its graph
Mean Value Theorem and Studying the Shape of Curves: MATH 151 4.3 Problems 1-6
Mean Value Theorem and properties of a graph
L'Hospital's Rule: MATH 171 Problems 7-9
Proving L'Hospital's Rule and using it to evaluate limits
Antiderivatives: MATH 171 Problems 4-6
Proving facts about antiderivatives and a physics application
Riemann Sums and Definite Integrals: MATH 151 5.2 Problems 6-12
Using Reimann sums and the Fundamental Theorem of Calculus
Riemann Sums and Definite Integrals: MATH 151 5.3 Problems 6-12
Using Riemann sums and the Fundamental Theorem of Calculus
Fundamental Theorem of Calculus: MATH 171 Problems 1-3
Proving and then applying the Fundamental Theorem of Calculus
Increasing, Decreasing, and Non Monotonic Sequences
Explaining increasing, decreasing, and non monotonic for sequences
Integration by Parts: MATH 172 Problems 1 & 2
Proving the formula for integration by parts and a reduction formula
WIR2 20B M251 V6
Determining the domain of a three-dimensional vector function
WIR2 20B M251 V8
Finding a vector equation for the tangent line to a three-dimensional vector function
WIR2 20B M251 V9
Finding the angle of intersection for two three-dimensional vector functions
WIR2 20B M251 V10
Finding the length of a three-dimensional curve
WIR2 20B M251 V11
Finding the curvature of a three-dimensional vector function
WIR3 20B M251 V1
Finding and sketching the domain of a function of two variables
WIR3 20B M251 V2
Finding and sketching the domain of a function of two variables
WIR4 20B M251 V9
Finding the absolute maximum and minimum values of a function of two variables on a rectangle
WIR4 20B M251 V10
Finding the absolute maximum and minimum values of a function of two variables on a triangular region
WIR8 20B M251 V1
Evaluating a line integral along half a circle
WIR8 20B M251 V2
Evaluating a line integral along a curve in space
WIR8 20B M251 V3
Evaluating a line integral along a curve
WIR8 20B M251 V4
Evaluating a line integral along a curve
WIR8 20B M251 V5
Evaluating a line integral along a curve in space
WIR8 20B M251 V6
Evaluating a line integral of a vector field along an curve
WIR8 20B M251 V7
Evaluating a line integral of a vector field along a curve in space
WIR8 20B M251 V8
Using a line integral to find the work done by a force field moving a particle along a curve
Matrix Derivative and Integral
Explaining how to find the derivative and integral of matrix and vector functions
MATH 152: Sequences Exercise 4
Finding the limit of a sequence
MATH 152: Sequences Exercise 6
Finding the limit of a sequence using logarithm properties
MATH 152: Sequences Exercise 7
Finding the limit of a sequence
Increasing, Decreasing, and Non Monotonic Sequences
Explaining increasing, decreasing, and non monotonic for sequences
MATH 152: Sequences Exercise 10
Determining if a sequence is increasing, decreasing, or non monotonic
WIR 20B M152 V45
Determining if a sequence converges or diverges
Functions of Several Variables Exercise V1
Evaluating and then finding and sketching the domain of a function of two variables
Functions of Several Variables Exercise V2
Finding and sketching the domain of a function of two variables
Functions of Several Variables Exercise V4
Sketching the level curves for a function of two variables
Functions of Several Variables Exercise V5
Sketching the level curves for a function of two variables
The Chain Rule (multivariable) Conceptual V1
Explaining the Chain Rule for multivariable functions
The Chain Rule (multivariable) Exercise V3
Using the Chain Rule for multivariable functions to find the rate a volume is changing
Finding the nth Taylor Polynomial Exercise
Finding the nth Taylor polynomial of the natural log function centered at 1
Approximation Using Taylor Polynomials Exercise
Using a Taylor polynomial to approximate the value of a function and estimating the error
The Chain Rule (multivariable) Conceptual V1
Explaining the Chain Rule for multivariable functions
Math 140 5.4 Exercise 4
Writing the domain of functions with radicals in interval notation
WIR2 20B M150 V7
Solving a rational equation and checking the solutions
WIR4 20B M150 V21
Solving an equation with logarithmic functions
WIR4 20B M150 V22
Solving an equation with logarithmic functions
WIR4 20B M150 V23
Solving an equation with logarithmic functions
WIR4 20B M150 V24
Solving an equation with logarithmic functions
WIR8 20B M150 V11
Solving an equation with logarithmic functions
Math 140 Exam 3 Review Exercise 1
Determining if a graph represents a function and finding the domain and range
Math 140 Exam 3 Review Exercise 4
Finding the properties of a quadratic function such as the vertex, axis of symmetry, intercepts, etc.
Math 140 Exam 3 Review Exercise 5
Finding the domain, intercepts, holes, and vertical asymptotes for a rational function
Math 140 Exam 3 Review Exercise 9
Finding the domain of a piecewise-defined function and evaluating it for given x-values
Math 140 Exam 3 Review Exercise 10
Finding properties of a polynomial function such as the degree, end behavior, y-intercept, etc.
Math 140 Exam 3 Review Exercise 11
Finding properties of a polynomial function such as the degree, end behavior, y-intercept, etc.
Math 140 Exam 3 Review Exercise 13
Stating the domain in interval notation of a function with radicals, fractions, and exponentials
Math 140 Exam 3 Review Exercise 24
Find the domain of a function in interval notation with a fraction and logarithm
Domain of a Rational Function
Finding the domain of a rational function
Domain of a Rational Function (2)
Finding the domain of a rational function
Domain of Function with Roots
Finding the domain of a function with a fraction and radicals
Domain of a Square Root Function
Finding the domain of a function with a quadratic inside a square root
Inverse of a Linear Function
Finding the inverse of a linear function and its domain
Inverse of a Square Root Function
Finding the inverse of a square root function and its domain
Inverse of a Rational Function
Finding the inverse of a rational function and its domain
Inverse of a Rational Function (2)
Finding the inverse of a rational function and its domain
Domain and x-intercepts of a Logarithmic Function
Finding the domain and x-intercepts of a logarithmic function
Domain and x-intercepts of a Logarithmic Function (2)
Finding the domain and x-intercepts of a logarithmic function
Solving an Equation with Logarithms
Solving a logarithmic equation using properties of logarithms
Solving an Equation with a Logarithmic Function
Solving a logarithmic equation using properties of logarithms
A Composition of Tangent and Arccosine
Evaluating a composition of tangent and arccosine
WIR 20B M152 V51
Determining if a series converges or diverges
WIR 20B M152 V63
Using the Alternating Series Test to determine if a series converges or diverges
List Comprehension and Patterns in Higher Derivatives in Python
Using Python's list comprehension tool to find several higher order derivatives of a function at once
Parametric Plots and Tangents at a Given t-value in Python
Using Python to find the tangent line to a parametric equation and plot the two graphs
Tangents to Parametrized Curves at a Given Point in Python
Using Python to plot a parametrized curve and its tangent line at a point
Finding Absolute (Global) Extrema in Python
Using Python to find the absolute maximum and minimum of a function on a closed interval
Finding and Graphing Tangent Lines to a Curve in Python
Using Python to find the equation of the tangent line to a curve and graphing the result
Finding Derivatives in Python
Finding derivatives in Python and solving for the rate of change of a force
Finding Horizontal Tangent Lines in Python
Finding when the tangent line to a function is horizontal in Python
Domain Restrictions
Explaining domain restrictions for denominators, even roots, and logarithms
Domain of Radical Functions Video 1
Finding the domain of even and odd roots
Domain of Radical Functions Video 2
Finding the domain of functions with even and odd roots
Domain of Rational Functions Video 1
Finding the domain of several rational functions
Domain of Rational Functions Video 2
Finding the domain of a rational function
Domain of Rational Functions Video 3
Explaining how to find any holes and vertical asymptotes of a rational function
Domain of Rational Functions Video 4
Finding the domain of a rational function using factoring
Domain of Logarithmic Functions Video 1
Finding the domain of a logarithmic function
Domain of Combinations of Functions Video 1
Finding the domain of a function with a denominator, square root, and logarithm
Domain of Combinations of Functions Video 2
Finding the domain of a function with a natural logarithm and denominator
Domain of Combinations of Functions Video 4
Finding the domain of a function with a root and a logarithm in the denominator
Linear Forms Video 2
Discussing properties of linear functions
Linear Graphs Video 1
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Making Linear Functions Video 2
Writing a linear equation of profit from a business word problem
Quadratic Form Video 1
Explaining the graph and properties for the parent function of quadratics
Quadratic Form Video 2
Discussing properties of quadratic functions including the vertex, domain, range, and end behavior
Properties of Rational Functions and Expressions Video 1
Discussing parent functions of rational functions and their properties
Properties of Rational Functions and Expressions Video 9
Explaining how to multiply and divide rational expressions
Properties of Rational Functions and Expressions Video 10
Performing algebraic operations with rational expressions and simplifying the answer
Solving Rational Equations Video 1
Solving equations that contain rational expressions
Solving Rational Equations Video 2
Solving an equation that contains rational expressions
Solving Rational Equations Video 3
Solving an equation that contains rational expressions
Properties of Radical Functions and Expressions Video 1
Explaining the general properties of even and odd root functions
Solving Radical Equations Video 1
Explaining how to solve radical equations and then solving example problems
Solving Radical Equations Video 2
Solving equations with even roots and checking the solutions
Solving Radical Equations Video 3
Solving equations with odd radicals
Solving Radical Equations Video 4
Solving equations with multiple radicals
Properties of Power and Exponential Expressions Video 4
Properties of exponential growth and decay functions
Properties of Power and Exponential Expressions Video 5
Properties of the exponential function with base e
Solving Power and Exponential Equations Video 1
Explaining how to solve equations with power and exponential terms
Properties of Logarithmic Functions and Expressions Video 2
Explaining the basic properties of logarithmic functions
Properties of Logarithmic Functions and Expressions Video 3
Expanding logarithmic expressions using logarithm rules
Properties of Logarithmic Functions and Expressions Video 4
Condensing a logarithmic expression into a single logarithm
Solving Logarithmic Equations Video 1
Explaining how to solve logarithmic equations
Solving Logarithmic Equations Video 2
Solving logarithmic equations with a single logarithm term
Solving Logarithmic Equations Video 3
Solving logarithmic equations with multiple logarithm terms
Solving Logarithmic Equations Video 4
Solving logarithmic equations with multiple logarithm terms on both sides
Splitting a Domain Into Two Pieces for a Double Integral
Evaluating a double integral over a given region by splitting it into two double integrals
Linear Forms Video 2
Discussing properties of linear functions
Linear Graphs Video 1
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Properties of Power and Exponential Expressions Video 4
Properties of exponential growth and decay functions
Properties of Power and Exponential Expressions Video 5
Properties of the exponential function with base e
Properties of Logarithmic Functions and Expressions Video 2
Explaining the basic properties of logarithmic functions
Derivatives of Exponential Functions
Explaining the formulas for the derivatives of exponential functions
Introduction to Riemann Sums
Estimating the area under a function using right-hand, left-hand, and midpoint Riemann sums
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative