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
|
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Solutions

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