5 Steps to a 5 AP Calculus BC 2019

CHAPTER 7

Big Idea 2: Derivatives

Graphs of Functions

and Derivatives

IN THIS CHAPTER

Summary:Many questions on the AP Calculus BC 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. Applica-

tions of Rolle’s Theorem, the Mean Value Theorem, and the Extreme Value Theorem

are shown. You will also learn to sketch the graphs of parametric and polar equations.

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

!Parametric and Polar Equations

!Vectors

7.1 Rolle’s Theorem, Mean Value Theorem, and Extreme

Value Theorem

Main Concepts:Rolle’s Theorem, Mean Value Theorem, Extreme Value Theorem

TIP • Set your calculator to Radians and change it to Degrees if/when you need to. Do not

forget to change it back to Radians after you have finished using it in Degrees.

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