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