# Activities

• • • ##### Subject Area

• Math: Calculus: Derivatives

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• ##### Other Materials
This is Activity 2 from the EXPLORATIONS Book:
Advanced Placement Calculus with the TI-89.

## 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.

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