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Graphing the Derivative of a FunctionWarm-up: Part 1 - What comes to mind when you think of the word 'derivative'?

Part 2 - Graph . Then find and graph it.

Graph of Graph of

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Directions: Given the function on the left, graph its derivative on the right.

Example 1

What if you're not given the equation of the original function?

1) Graph of Graph of

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2)Graph of

Graph of

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Graph of Graph of 3)

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What about these graphs? It would be difficult to come up with the equations. Can you graph their derivatives?

http://www.khanacademy.org/math/calculus/e/derivative_intuitionAt this time, go to this website on your iPads:

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What do you notice about the answer column on the right and the graph?

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Example 3Directions: Given the function on the left, graph its derivative on the right.

Graph of Graph of

What do you notice about the graph of when is negative?

What do you notice about the graph of when is positive?

What do you notice about the graph of when is zero?

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Which graph on the right is the derivative graph of the function below on the left?

Example 6: Multiple Choice

A.

B.

C.

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Which graph on the right is the derivative graph of the function below on the left?

Example 7: Multiple Choice

A.

B.

C.

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Graphing a Function Given its Derivative Graph

Graph of Graph of

Directions: The function on the left is . Graph on the right.

What type of function would be?

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Directions: The function on the left is . Graph on the right.

Example 8

Graph of Graph of

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Example 9: Given the graph of the derivative, sketch a possible graph for the function.

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Example 10: Multiple ChoiceThe function on the left is . Which graph on the right is ?

A.

B.

C.

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Example 11: Multiple ChoiceThe function on the left is . Which graph on the right is ?

A.

B.

C.

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2. is increasing when is ___________________.

1. is zero when is _____________________.

3. is negative when is______________________.

Recalling the Lesson: Fill in the blank.

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Use these websites to practice...

http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_try_to_graph.html

http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_app_1_graph_AD.html

http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_matching.html

http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_matching_antiderivative.html

Practice graphing a derivative given the graph of the original function:

Practice graphing an original function given a derivative graph:

Multiple Choice: Graphing a derivative.

Multiple Choice: Graphing an original function given a derivative.