In this activity, you will study what the graph of the first and second derivative tells about a function. The red function is your original function, with a movable point. 1) Check the "1st Derivative" box. Move point A and the 1st derivative will be plotted in blue. Answer the following questions: a) The x-coordinate of point B matches the x-coordinate of point A. How is the y-coordinate of point B determined? (You may want to use some tools to test this.) b) What is significant about the roots of the derivative? c) Is there anything else you can say about how the graph of the derivative relates to the red graph? Click on the Reset Button to clear the graph and do part 2 below.

2) Check the "2nd Derivative" box. Drag point A to graph the 2nd derivative. a) What is significant about the roots of the 2nd derivative? b) What else can you say about how the graph of the 2nd derivative relates to the graph of the function? Make as many generalizations as you can about the 1st and 2nd derivative.