Education Technology

Symmetric Secant

Published on 12/05/2011

Activity Overview

Investigate the symmetric secant line to provide an estimate for the derivative of a function at a point.

Objectives

  • Use the slope of the symmetric secant line to approximate the derivative of a function at a point and generalize properties of functions that affect the accuracy of these estimates
  • Explain the relationship between the symmetric difference quotient and the standard difference quotient used to calculate the derivative of a function at a point both graphically and numerically

Vocabulary

  • secant and tangent line
  • difference quotient
  • derivative

About the Lesson

This lesson provides a visual demonstration of how and when the symmetric secant line can be used to provide a reasonable estimate for the derivative of a function at a point. As a result, students will:

  • Explore a variety of function graphs to observe how the slope of the symmetric secant line comes closer to approximating the slope of the tangent line as the value of h decreases.
  • Use the symmetric secant line to estimate derivatives at a point and compare these estimates to other numerical and analytic methods.
  • Discover the importance of considering the function graph when estimating derivatives by exploring instances in which the symmetric difference quotient provides a value even though the derivative of the function does not exist.