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Activity Overview

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

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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
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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
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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