Ch 3 - Applications of Differentiation
Chapter 3 PDF Resource
| calculus_chapter_3.pdf |
Lecture Notes & Videos
Section 3-1 (Day 1)
Extrema of an Interval
-----VIDEO: (Review) Solving Trig Equations on a TI-84 Calculator
-----VIDEO: Definition of Critical Numbers and 3 Examples of Finding Critical Numbers
-----VIDEO: Definition of Critical Numbers and Finding Critical Numbers from Graphs
Section 3-1 (Day 2)
More on Extrema
-----VIDEO: Extreme Value Theorem: Finding Absolute Extrema on a Closed Interval
Section 3-2 (Day 1)
Rolle's Theorem
----- VIDEO: Rolle's Theorem
Rolle's Theorem
A Graphical Representation of Rolle's Theorem
Section 3-2 (Day 2)
Mean Value Theorem
----- VIDEO: Mean Value Theorem (MVT) for Derivatives
Section 3-3
Increasing & Decreasing Functions and The First Derivative Test
----- VIDEO: Finding Increasing & Decreasing Intervals & Max/Min Points and First Derivative Test
Section 3-4 (Day 1)
Concavity
----- VIDEO: Definition of Concavity & How to Test for It ❖ Tangent Line Requirement in Definition - Part 1 of 2
----- VIDEO: Testing for Concavity & Finding Points of Inflection - Part 2 of 2
Section 3-4 (Day 2)
Second Derivative Test
-----VIDEO: 2nd Derivative Test
Section 3-5
Limits at Infinity
-----VIDEO: Limits at Infinity
-----VIDEO: More Limits at Infinity
-----VIDEO: Short-Cut Tricks for Limits at Infinity
Section 3-6
Curve Sketching
-----VIDEO: Curve Sketching Example
Section 3-7 (Days 1 and 2: Combined)
Optimization Problems showing a Simple 6 Step Process.
-----VIDEO: Optimization Problem
Section 3-8
Newton's Method
-----VIDEO: A Visual Representation of Newton's Method
Section 3-9
Differentials & Linear Approximation
-----VIDEO: Linear Approximation - Used to Find an Approximation
Extrema of an Interval
-----VIDEO: (Review) Solving Trig Equations on a TI-84 Calculator
-----VIDEO: Definition of Critical Numbers and 3 Examples of Finding Critical Numbers
-----VIDEO: Definition of Critical Numbers and Finding Critical Numbers from Graphs
Section 3-1 (Day 2)
More on Extrema
-----VIDEO: Extreme Value Theorem: Finding Absolute Extrema on a Closed Interval
Section 3-2 (Day 1)
Rolle's Theorem
----- VIDEO: Rolle's Theorem
Rolle's Theorem
A Graphical Representation of Rolle's Theorem
Section 3-2 (Day 2)
Mean Value Theorem
----- VIDEO: Mean Value Theorem (MVT) for Derivatives
Section 3-3
Increasing & Decreasing Functions and The First Derivative Test
----- VIDEO: Finding Increasing & Decreasing Intervals & Max/Min Points and First Derivative Test
Section 3-4 (Day 1)
Concavity
----- VIDEO: Definition of Concavity & How to Test for It ❖ Tangent Line Requirement in Definition - Part 1 of 2
----- VIDEO: Testing for Concavity & Finding Points of Inflection - Part 2 of 2
Section 3-4 (Day 2)
Second Derivative Test
-----VIDEO: 2nd Derivative Test
Section 3-5
Limits at Infinity
-----VIDEO: Limits at Infinity
-----VIDEO: More Limits at Infinity
-----VIDEO: Short-Cut Tricks for Limits at Infinity
Section 3-6
Curve Sketching
-----VIDEO: Curve Sketching Example
Section 3-7 (Days 1 and 2: Combined)
Optimization Problems showing a Simple 6 Step Process.
-----VIDEO: Optimization Problem
Section 3-8
Newton's Method
-----VIDEO: A Visual Representation of Newton's Method
Section 3-9
Differentials & Linear Approximation
-----VIDEO: Linear Approximation - Used to Find an Approximation
Additional Handouts
Blank Curve Sketching Sheet with Chart
Ch 3 Study Guide
This handout includes a general overview of all of the major points in the chapter.
Curve Sketching Notes
This handout summarizes curve sketching.
Newton's Method
This handout gives a visual representation of Newton's Method.
Another Ch 3 Study Guide
This handout including examples with Linear Approximation, Newton's Method, and Differentials.
Summary of 4 Theorems
This handout summarizes the Extreme Value Theorem, the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem.
Using the Graph of f'(x)
This handout shows you how to find Max's and Min's from the graph of the derivative.
4 Major Calculus Theorems with Examples
This handout includes a short summary of the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem. It also includes examples.
Ch 3 Study Guide
This handout includes a general overview of all of the major points in the chapter.
Curve Sketching Notes
This handout summarizes curve sketching.
Newton's Method
This handout gives a visual representation of Newton's Method.
Another Ch 3 Study Guide
This handout including examples with Linear Approximation, Newton's Method, and Differentials.
Summary of 4 Theorems
This handout summarizes the Extreme Value Theorem, the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem.
Using the Graph of f'(x)
This handout shows you how to find Max's and Min's from the graph of the derivative.
4 Major Calculus Theorems with Examples
This handout includes a short summary of the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem. It also includes examples.
Practice Problems
Worksheets
Sections 3-1 to 3-2 Review WS
Miscellaneous Review Ch 1 thru Section 3-2 WS
Miscellaneous Review Ch 1 thru Section 3-2 WS KEY
Sections 3-1 thru 3-4 Review WS
Sections 3-1 thru 3-4 Review WS KEY
AP Limits & Continuity Practice WS
Curve Sketching WS #1
Curve Sketching WS #2
Limits of Functions as X approaches Infinity WS #1
Optimization WS #1
Limits of Functions as X approaches Infinity WS #2
Curve Sketching WS #3
Optimization WS #2
Review WS Sections 3-5 to 3-7 (Version 2)
Review WS Sections 3-5 to 3-7 (Version 2) KEY
Chapter 1 Review WS
Limit Review WS
Derivative WS
Open Ended AP Questions WS #3
Mean Value Theorem WS
Linear Approximation WS #1
Open Ended AP Questions WS #4
Rolle's Theorem WS
Chapter 3 Review WS
Chapter 3 Review WS KEY
Related Rates Review WS
Miscellaneous Review Ch 1 thru Section 3-2 WS
Miscellaneous Review Ch 1 thru Section 3-2 WS KEY
Sections 3-1 thru 3-4 Review WS
Sections 3-1 thru 3-4 Review WS KEY
AP Limits & Continuity Practice WS
Curve Sketching WS #1
Curve Sketching WS #2
Limits of Functions as X approaches Infinity WS #1
Optimization WS #1
Limits of Functions as X approaches Infinity WS #2
Curve Sketching WS #3
Optimization WS #2
Review WS Sections 3-5 to 3-7 (Version 2)
Review WS Sections 3-5 to 3-7 (Version 2) KEY
Chapter 1 Review WS
Limit Review WS
Derivative WS
Open Ended AP Questions WS #3
Mean Value Theorem WS
Linear Approximation WS #1
Open Ended AP Questions WS #4
Rolle's Theorem WS
Chapter 3 Review WS
Chapter 3 Review WS KEY
Related Rates Review WS
Study Guides
Interactive Animations
Calculus is the study of change. The ability to change a parameter and immediately see the result can demonstrate that change and how things are related during that change. Many of these concepts are much easier to explain if that change, the motion, can be visually demonstrated in class. Therefore, this is a perfect place for the use of computer animations.
All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.
All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.
Please be patient! It takes awhile for these to load.
Widen the browser, if necessary, to see the entire animation.
Widen the browser, if necessary, to see the entire animation.
Rolle's Theorem & Mean Value Theorem
An illustration of the Mean Value Theorem. Rolle's Theorem is included as a special case.
Rolle's Theorem: An Interactive Exploration
This applet shows interactively the points in which the Rolle's Theorem for a real function holds true.
You can type the function expression in the f(x)field, and the interval start and end points in the a and b fields. Move point c on the x-axis in order to view the different positions assumed by the tangent line to the function graph.
Verify whether the following functions satisfy the hypothesis of Rolle's Theorem in the given intervals, and hence find the point(s) c as prescribed by the theorem:
f(x) = 1 + |x| on [-1,1]
f(x) = -x^2 - x + 2 on [-1,0]
You can type the function expression in the f(x)field, and the interval start and end points in the a and b fields. Move point c on the x-axis in order to view the different positions assumed by the tangent line to the function graph.
Verify whether the following functions satisfy the hypothesis of Rolle's Theorem in the given intervals, and hence find the point(s) c as prescribed by the theorem:
f(x) = 1 + |x| on [-1,1]
f(x) = -x^2 - x + 2 on [-1,0]
Optimization of Rectangles - Area & Perimeter
This applet allows students to investigate the optimal area and optimal perimeter of a rectangle. Drag the vertices Width and Length to change the dimensions of the rectangle.
What is the optimal area of a rectangle?
Find as many pairs of dimensions as you can that give a perimeter of 20cm.
Which of these pairs gives the optimal area?
What is the optimal perimeter of a rectangle?
Find as many pairs of dimensions as you can that give an area of 36 sq. cm.
Which of these pairs gives the optimal perimeter?
What is the optimal area of a rectangle?
Find as many pairs of dimensions as you can that give a perimeter of 20cm.
Which of these pairs gives the optimal area?
What is the optimal perimeter of a rectangle?
Find as many pairs of dimensions as you can that give an area of 36 sq. cm.
Which of these pairs gives the optimal perimeter?
Optimization - Maximizing Area
Maximizing the Area of a 3-Sided Rectangle
What is the length and width of the 3-sided rectangle that maximizes the area?
What is the length and width of the 3-sided rectangle that maximizes the area?
Newton's Method
This is a dynamic illustration of Newton's Method for approximating roots of functions. Drag point x1 to change the initial guess and see how the subsequent approximations change.
Use the slider to change to another example.
Use the slider to change to another example.
Newton's Method - User Defined Function
This dynamic illustration demonstrates the procedure involved in the use of Newton's method for approximating the roots of an equation.
In this version, the user can enter their own equation.
In this version, the user can enter their own equation.
