Absolute Extrema on a Closed Interval 2
Finding the absolute maximum and absolute minimum of a rational function on two closed intervals
tags:
Absolute Maximum Absolute Minimum Critical Value Derivative Domain How-To Calculus Quotient Rule Rational FunctionAbsolute Extrema on a Closed Interval
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: Find the absolute maximum and minimum of the function \(f(x)=\dfrac{x^3}{x^2-1}\) on each of the following intervals.
- \([-0.5,0.5]\)
- \(\left[\dfrac{4}{3},6\right]\)
- An absolute minimum of \(-\frac{1}{6}\) at \(x=0.5\), an absolute maximum of \(\frac{1}{6}\) at \(x=-0.5\)
- An absolute minimum of \(\frac{3\sqrt{3}}{2}\approx 2.598\) at \(x=\sqrt{3}\), an absolute maximum of \(\frac{216}{35}\approx 6.171\) at \(x=6\)
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Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40
Review of derivatives and tangent lines to functions and vector equations
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 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
Limits: MATH 151 Problems 6-20
Evaluating limits of functions
Limits: MATH 151 Problems 6-20
Evaluating Limits of Functions
Limits and Asymptotes: MATH 151 2.6 Problems 7-11
Limits at infinity and asymptotes, along with physics applications
Approximations and Exponentials: MATH 151 2.6 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Limits and Asymptotes: MATH 151 2.7 Problems 7-11
Limits at infinity, asymptotes, and tangent lines
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 36-40
Review of derivatives and tangent lines to functions and vector equations
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 36-40
Derivatives and tangents to curves
Vectors and Derivatives: MATH 151 3.4 Problems 1-8
Derivatives and vectors with some physics applications
Approximations and Exponentials: MATH 151 3.4 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Implicit Differentiation: MATH 151 3.5 Problems 10-13
Implicit differentiation and finding tangent lines
Vectors and Derivatives: MATH 151 3.7 Problems 1-8
Derivatives and vectors with some physics applications
Derivatives and Applications: MATH 151 3.9 Problems 9-15
Tangent lines to parametric equations and related rates examples
Integration by Substitution: MATH 151 5.5 Problems 13 & 14
Examples of integration by substitution
MLC WIR 20B M151 week3 #16
Finding the vertical and horizontal asymptotes for a rational function
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 #1i
Using the Product Rule 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 #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 #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 #1ab
Using the Product and Chain Rule 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 #11
Using a linear approximation to approximate the value of a function
MLC WIR 20B M151 week6 #17
Finding the linear approximation for 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 #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 #8a
Evaluating a limit using logarithm properties
MLC WIR 20B M151 week9 #8b
Evaluating a limit with an indeterminate difference using a common denominator
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 #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 week9 #1
Determining the properties of a function from the graph of its derivative
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
MLC WIR 20B M151 week10 #24b
Evaluating a definite integral by first simplifying the integrand
MLC WIR 20B M151 week10 #8a
Evaluating the limit at infinity of a rational function
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 #6a
Evaluating a a limit from the left for a rational function
MLC WIR 20B M151 week10 #6b
Evaluating the limit of a rational function by factoring and cancelling
Review for the Common Exam: MATH 152 Exam 1 a Review Problems 1-4
Reviewing u-Substitution
Review for the Common Exam: MATH 152 Exam 1 b Review Problem 36
Review of partial fractions
Review for the Common Exam: MATH 152 Exam 1 b Review Problems 34 & 35
Review of partial fractions
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 V76
Finding a power series representation for a function
MATH 152: u-Substitution Exercise 3
Using u-substitution to integrate a rational function
WIR 20B M152 V2
Integrating a rational function using u-substitution
WIR 20B M152 V3
Integrating a rational function using u-substitution
Cases for Partial Fraction Decomposition
Explaining all four cases of partial fraction decomposition
MATH 152: Partial Fraction Decomposition Exercise 1
Using partial fraction decomposition to rewrite and then integrate a rational function
MATH 152: Partial Fraction Decomposition Exercise 2
Using partial fraction decomposition to rewrite and then integrate a rational function
MATH 152: Partial Fraction Decomposition Exercise 3
Using partial fraction decomposition to rewrite and then integrate a rational function
MATH 152: Partial Fraction Decomposition Exercise 5
Using partial fraction decomposition to rewrite and then integrate a rational function
MATH 152: Partial Fraction Decomposition Exercise 6
Using partial fraction decomposition to rewrite and then integrate a rational function
Vector Functions: MATH 171 Problems 1 & 2
Proving a certain parameterization gives the unit circle and showing vector equations of lines are parallel
Parametric Curves: MATH 151 J.3 Problems 1-5
Cartesian equations and parametric equations of curves
Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3
Proving facts about the derivatives of vector functions including the product rule
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
Derivatives and Applications: MATH 171 Problems 7 & 8
Calculating slopes of tangent lines to parametric curves
Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40
Review of derivatives and tangent lines to functions and vector equations
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 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
Limits: MATH 151 Problems 6-20
Evaluating limits of functions
Limits: MATH 151 Problems 6-20
Evaluating Limits of Functions
Continuity: MATH 171 Problems 6 & 7
Proving a piecewise function and a polynomial are continuous
Approximations and Exponentials: MATH 151 2.6 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Limits and Asymptotes: MATH 151 2.6 Problems 7-11
Limits at infinity and asymptotes, along with physics applications
Limits and Asymptotes: MATH 151 2.7 Problems 7-11
Limits at infinity, asymptotes, and tangent lines
Review for the Common Exam: MATH 151 3.1 Exam 1 Review Problems 36-40
Review of derivatives and tangent lines to functions and vector equations
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
Differentials: MATH 171 Problems 1 & 2
Proving facts about differentials including a product rule
Review for the Common Exam: MATH 151 3.2 Exam 1 Review Problems 36-40
Derivatives and tangents to curves
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
Vectors and Derivatives: MATH 151 3.4 Problems 1-8
Derivatives and vectors with some physics applications
Approximations and Exponentials: MATH 151 3.4 Problems 7-14
Approximation and Newton's Method, and limits and derivatives of exponential functions
Implicit Differentiation: MATH 151 3.5 Problems 10-13
Implicit differentiation and finding tangent lines
Derivatives of Logarithmic Functions: MATH 171 Problems 1-3
Proving the derivative of ln(x) and the power and product rules using logarithmic differentiation
Derivatives and Applications: MATH 151 3.9 Problems 9-15
Tangent lines to parametric equations and related rates examples
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
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
Fundamental Theorem of Calculus: MATH 171 Problems 1-3
Proving and then applying the Fundamental Theorem of Calculus
Integration by Substitution: MATH 151 5.5 Problems 13 & 14
Examples of integration by substitution
Review for the Common Exam: MATH 152 Exam 1 a Review Problems 1-4
Reviewing u-Substitution
Review for the Common Exam: MATH 152 Exam 1 b Review Problem 36
Review of partial fractions
Review for the Common Exam: MATH 152 Exam 1 b Review Problems 34 & 35
Review of partial fractions
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
Integration Using Partial Fractions: MATH 172 Problems 8 & 9
Finding a partial fraction decomposition and integrating using partial fractions
Cases for Partial Fraction Decomposition
Explaining all four cases of partial fraction decomposition
WIR2 20B M251 V7
Finding the limit 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
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
WIR 20B M152 V45
Determining if a sequence converges or diverges
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
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
Maximum and Minimum Value (multivariable) Exercise V3
Finding the minimum surface area for a box by minimizing a function of two variables
Lagrange Multipliers Exercise V3
Using Lagrange Multipliers to find the minimum values of a function subject to a constraint
Lagrange Multipliers Exercise V4
Using Lagrange Multipliers to find the largest box that can be inscribed in an ellipsoid
Cases for Partial Fraction Decomposition
Explaining all four cases of partial fraction decomposition
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
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 7
Compute and simplify the difference quotient for a rational function
Math 140 Exam 3 Review Exercise 8
Finding the maximum profit for a word problem given the cost and price-demand equation
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
Simplifying a Rational Expression
Simplifying a rational expression
Subtracting Rational Expressions
Adding and then simplifying two rational expressions
Multiplying Rational Expressions
Multiplying two rational expressions and then simplifying
Dividing Rational Expressions
Dividing rational expressions and then simplifying the answer
Adding Rational Expressions
Adding two rational expressions and then simplifying the answer
Holes and Asymptotes of Rational Functions
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Holes and Asymptotes of Rational Functions (2)
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Matching a Rational Function with its Graph
Matching a rational function with its graph
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
Function Composition with a Rational Function
Finding the composition of a rational function and a quadratic
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
Difference Quotient of a Rational Function
Finding and simplifying the difference quotient for a rational function
Difference Quotient of a Square Root Function
Finding and simplifying the difference quotient for a square root function
Solving an Inequality with a Rational Function
Solving an inequality with a rational expression by factoring and using a sign diagram
Solving an Inequality with a Sum of Rational Functions
Solving an inequality with two rational expressions using a sign diagram
Solving an Inequality with by Finding a Least Common Denominator
Solving an inequality with a rational expression using a sign diagram
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
Creating and Manipulating Symbolic Expressions in Python
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
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 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 Logarithmic Functions Video 1
Finding the domain of a logarithmic function
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
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 4
Finding horizontal asymptotes for rational functions
Properties of Rational Functions and Expressions Video 5
Determining the end behavior and horizontal asymptotes for rational functions
Properties of Rational Functions and Expressions Video 2
Finding horizontal asymptotes for rational functions
Properties of Rational Functions and Expressions Video 3
Explaining how to do polynomial long division
Properties of Rational Functions and Expressions Video 7
How to simplify rational expressions
Properties of Rational Functions and Expressions Video 8
Adding and subtracting rational expressions by finding a common denominator
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 14-25
Review of limits, continuity, and the Intermediate Value Theorem