NAHS AP Calculus Unit 4

Applications of Differentiation
Day Notes Critical Homework Videos
1 Extrema on an Interval

Lesson 1

Solutions Extreme Value Theorem
Applying the Extreme Value Theorem
Finding Critical Numbers
2 Rolle’s Theorem & Mean Value Theorem(MVT) Lesson 2 Solutions Rolle's Theorem (and proving a horiz. tangent line)
Theory behind the Mean Value Theorem
Applying the Mean Value Theorem Example
3 Increasing and Decreasing Functions & The First Derivative Test Lesson 3 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
4 Concavity & the Second Derivative Test Lesson 4 Solutions Concavity and Inflection Points
Finding Intervals of Concavity(Up & Down)
Finding Intervals of Concavity Using the First Derivative Graph
Analyzing Concavity (Graphical)
5 Linearization and Tangent Line Approximation Lesson 5 Solutions Tangent Line Approximation
Tangent Line Approximation Examples
6 Optimization Lesson 6 Solutions Optimization Procedures/Plan
Optimization of Profit
Optimization of Geometry
Optimization of Volume (1 With Calculator) & (2 with Calculus)