**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

You can type the

f(x) = 1 + |x| on [-1,1]

f(x) = -x^2 - x + 2 on [-1,0]

*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]

**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.

Find as many pairs of dimensions as you can that give a perimeter of 20cm.

Which of these pairs gives the optimal area?

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?

**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.