NAHS AP Calculus Unit 3

Applications of Differentiation
Day Notes Critical Homework Videos
1

 

Related Rates

 

Lesson 1 Critical HW

Solutions

Related Rate Examples #1 & #2 & #3 & #4 & #5 & #6
2

 

Average & Instantaneous Rate of Change

 

Lesson 2 Critical HW

Solutions

Using Average ROC to Approximate Instantaneous ROC Video 1& Video 2& Video 3
3

Theorems Involving Differentiation

Lesson 3 Critical HW

Solutions

Extreme Value Theorem
Applying the Extreme Value Theorem
Finding Critical Numbers
Rolle's Theorem (and proving a horiz. tangent line)
Theory behind the Mean Value Theorem
Applying the Mean Value Theorem Example
4

Increasing and Decreasing Functions & The First Derivative Test

Lesson 4 Critical HW

Solutions

Intervals of Increase/Decrease
Finding Intervals of Increase/Decrease and Local Min/Max.
AP Example of Finding Intervals of Increase
Using First Derivative Test to Determine Relative Min/Max.
Interpreting the First Derivative Graph
Examples of Reading a First Derivative Graph to Determine Qualities of the Original Graph
5

Concavity & the Second Derivative Test

Lesson 5 Critical HW

Solutions

Concavity and Inflection Points
Finding Intervals of Concavity(Up & Down)
Finding Intervals of Concavity Using the First Derivative Graph
Analyzing Concavity (Graphical)
6

Optimization

Lesson 6 Critical HW

Solutions

Optimization Procedures/Plan
Optimization
Optimization of Profit
Optimization of Geometry
Optimization of Volume (1 With Calculator) & (2 with Calculus)
7

 

Inverse Functions & Slope

 

Lesson 7 Critical HW

Solutions

Slopes of Inverse Functions
8

Linearization and Tangent Line Approximation

Lesson 8 Critical HW

Solutions

Tangent Line Approximation
Tangent Line Approximation Examples
9

 

L'Hopitals Rule

 

Lesson 9 Critical HW

Solutions

L'Hopitals Rule Part 1

L'Hopitals Rule Part 2

 

 

Review for Unit 3 Major Assessment

 

 

Solutions