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


  • 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




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    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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