AP Calculus BC Knowledge Review: Graphs of Functions and Derivatives

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Introduce:

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. Applications 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

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

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