5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 17:21

CHAPTER

8

Big Idea 2: Derivatives

Graphs of Functions

and Derivatives

IN THIS CHAPTER

Summary:Many questions on the AP Calculus AB exam involve working with graphs
of a function and its derivatives. In this chapter, you will learn how to use derivatives
both algebraically and graphically to determine the behavior of a function.
Applications of Rolle’s Theorem, the Mean Value Theorem, and the Extreme Value
Theorem are also shown.
Key Ideas
KEY IDEA !Rolle’s Theorem, Mean Value Theorem, and Extreme Value Theorem

!Test for Increasing and Decreasing Functions

!First and Second Derivative Tests for Relative Extrema

!Test for Concavity and Point of Inflection

!Curve Sketching

!Graphs of Derivatives

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