Education Technology

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.

    Follow the Activity procedures:

  • 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