Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Limits of Functions

9-12

75 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Other Materials
This is Activity 7 from the EXPLORATIONS Book:
Calculus Activities.

## Graph of Functions and Their Derivatives

#### Activity Overview

In this activity, students observe the derivative as an indicator of increasing/decreasing function behavior. They also see that the derivative is an indicator of local maxima/minima function behavior. Students learn to associate the graph of a function with its derivative.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 67 - 72 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Graph the function and its derivative
• Examine the behavior of the function, and its derivative as the function increases and decreases
• Locate the local maximum and minimum values from the graph of the function
• Observe the graph of the derivative at the local maximum and minimum values
• Examine other functions in the same way
• #### After the Activity

Students' will collect data and analyze the results.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary