Education Technology

Application of the Derivative

Published on 06/09/2008

Activity Overview

In this activity, students learn and explore two common applications of the derivative: optimization and related rate.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 27 - 32 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:
    Designing a Cylinder:

  • Define the surface area as a function of the radius
  • Compute the first derivative, set it equal to zero and determine the minimum point
  • Use minimization commands and obtain the result on a graph


  • Related Rates for a Sphere:
  • Consider volume and radius as a function of time
  • Define the volume as a function of the radius
  • Compute derivative and substitute values for rate and radius
  • After the Activity

    Students will complete the practice exercise problems.

    Review student results:

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