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

