Activity Detail
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Differentiation
 


Activity Overview

In this activity, students explore estimated and exact results for derivatives, tangent lines, implicit differentiation, and symbolic differentiation.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 15 - 26 from the attached PDF file for your class

    		•

    		During the Activity

    		Distribute the pages to the class.

    Follow the Activity procedures:
    Finding Slope and the Tangent Line:
  • Enter the function and find average rate of change with an arbitrary increment
  • Find the numerical derivative and graph to find the tangent line

  • Find the numerical derivative and graph the function
  • Compute a point on the graph and estimate the value of the derivative
  • Plot the tangent line


    • Exact Derivatives:
  • Explore derivatives with limits and built-in derivative command


    • Implicit Differentiation:
  • Use implicit theorem to compute the derivative in terms of x and y
  • Evaluate the derivative for different values of x and y
  • Compute the derivative directly by writing y as a function of x


    • Solve for the Function y(x):
  • Find values of y that give the function a value of zero and differentiate
  • Evaluate the derivative for a particular value of x
  • Graph the function and draw tangent lines


    • Symbolic Differentiation:
  • Use the differentiate command with undefined functions

    		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 2 from the EXPLORATIONS Book:
    Advanced Placement Calculus with the TI-89.

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