Differentiation

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Calculus: Derivatives

Math: AP Calculus: AP Calculus

Level

9-12

Activity Time

60 Minutes

TI Calculator

TI-89 / TI-89 Titanium

Other Materials

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

Resource Types

Lessons

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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

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix A PDF Teacher Notes Appendix B PDF Teacher Notes Appendix C PDF Teacher Notes Appendix D PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Calculus: Derivatives

Math: AP Calculus: AP Calculus

Level

9-12

Activity Time

60 Minutes

TI Calculator

TI-89 / TI-89 Titanium

Other Materials

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

Resource Types

Lessons

Report an Issue

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Differentiation

Differentiation

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