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