Increasing and Decreasing and Local Extrema
Finding the intervals where a function is increasing/decreasing and the local extrema
Finding Critical Values
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 critical values of the following functions, if they exist.
- \(f(x)=x^5-5x^4-20x^3+100\)
- \(f(x)=\dfrac{x^3}{x^2-9}\)
- \(x=-2,0,6\)
- \(x=-\sqrt{27},0,\sqrt{27}\)
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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 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 22-24
Optimization problems
Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30
Antiderivatives and physics applications
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
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: MATH 171 Problems 1 & 2
Proving facts about differentials including a product rule
Differentials and Approximations: MATH 151 3.10 Problems 1-6
Differentials, linear approximations and quadratic approximations
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
Inverse Trigonometric Functions: MATH 151 Problems 9-12
Properties and derivatives of inverse trigonometric functions
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: MATH 171 Problems 6-8
Using the Mean Value Theorem to prove facts about functions
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
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
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 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
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
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
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
WIR 20B M152 V45
Determining if a sequence converges or diverges
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
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
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
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
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
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions