This lesson helps students learn how to graph the derivative of a function, given a graph of the function. Students also learn how to interpret the graph of the derivative and they make the connection between the derivative of the position function and the velocity function. Increasing and decreasing functions are also introduced. Finally, students learn how to estimate derivatives from a table of values and then use those values to create a graph of the derivative.

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

Detailed answer keys are included.

The topics covered include:

-Analyzing Derivatives of Polynomials Graphically

-Graphing the Derivative Function

-Practice with Graphing the Derivative Function

-Increasing and Decreasing Functions

-Working with Increasing and Decreasing Functions

-Interpreting the Graph of the Derivative Function

-Working with the Position Function

-Estimating Derivatives

In this product, you will find the following:

-Powerpoint Presentation (23 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 Derivatives. The complete unit includes the following:

-Rates of Change

-The Derivative Function

-Derivatives of Polynomials

-Graphing the Derivative

-Higher Derivatives

-Differentiability