Education Technology

Local Linearity, Differentiability and Limits of Difference Quotients

Activity Overview

In this activity, students explore a graphical feature of some functions called local linearity. They also investigate the link between local linearity and differentiability through several examples.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 57 - 62 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Enter the function and graph it
  • Draw a tangent line to the graph and write the equation of the line
  • Use the Zoom function and observe if local linear points exist
  • Investigate the difference quotient numerically using parametric equations
  • 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