Sketching Derivatives of Freehand Drawn Functions

Shown below are 3 hand-drawn function graphs. Each function is named . Complete the following steps for the first graph (for now).

• Use the MOVE tool to drag point A along .
• Use the POINT tool to plot the locations of several key points that you know lie on the graph of the derivative of .

Note: The next 3 steps are illustrated in the video below the first app.

• Use the PEN tool to draw a sketch of what you think the graph of looks like.
• Plot the point . This point lies on the graph of .
• Right click on the point you plotted in the last step. Select SHOW TRACE. Then drag A around the graph slowly.

Question: Explain why the point lies on the graph of . Also, how did you do?