Education Technology

# Activities

## Application of the Derivative

#### 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.

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