Activity Detail

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	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

Activity Downloads:

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

Other Downloads

view standards alignment
view textbook alignment

Subject Area:
Math : Calculus : Derivatives

Author:
Texas Instruments

Level:
9-12

Activity Time:
60 Minutes

Device:
TI-89 / TI-89 Titanium

Apps:

Software:

Accessories:

Other:
This is Activity 3 from the EXPLORATIONS Book:
Advanced Placement Calculus with the TI-89.

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