Calculus-Making Observations about the Function and Its Derivatives from Graphs

This discovery activity is made up of 5 part plus a closing question.

Part I: Students graph a function and its derivative. From the two graphs students observe that when the graph of the derivative of y1 is positive the graph of y1 is increasing and that when the graph of the derivative of y1 is negative the graph of decreasing.

Part II: In part I students studied a function with a minimum. In this part students will repeat the same observations but with a function that has a maximum.

Part III: Students will compare the value of a derivative of y1 with the behavior of y1.

Part IV in this part students will describe the conditions that mujst be true about a function y1 for a maximum to exist.

Closing Part: From a graph of f’ students will descdribe where the original function f is increasing and decreasing. They will also draw a sketch of f”.

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