AP Calculus: The First and Second Derivative Tests Complete Lesson

This lesson introduces the First and Second Derivative Tests in the context of polynomials. (The lesson on Curve Sketching uses these tests to examine other types of functions.) The lesson begins with a review of increasing and decreasing functions as well as critical numbers. Then, the First Derivative Test is introduced, along with an application. After that, concavity and inflection points are introduced. Finally, the Second Derivative Test is shown, along with an example.

This lesson is appropriate for both AP Calculus AB and BC.

Detailed answer keys are included.

The topics covered include:

-Review: Increasing and Decreasing Functions

-The First Derivative Test

-Using the First Derivative Test

-Concavity

-Inflection Points

-Applying Inflection Points and Concavity

-The Second Derivative Test

-Using the Second Derivative Test

In this product, you will find the following:

-Powerpoint Presentation (31 slides)

-Guided Notes (4 pages, a "filled in" copy is also included)

-Do Now Slips (4 slips on one page, answers included)

-Exit Ticket Slips (4 slips on one page, answers included)

-Homework Assignment (2 pages, a detailed answer key is included)

This lesson is part of a larger unit on Applications of Derivatives. The complete unit includes the following:

-Linear Approximation and Differentials

-Related Rates

-Maximum and Minimum Values

-The Mean Value Theorem

-The First and Second Derivative Tests

-L'Hospital's Rule

-Curve Sketching

-Optimization Problems

-Motion Problems

-Antiderivatives