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.[br][br]1) Check the "1st Derivative" box. Move point A and the 1st derivative will be plotted in blue. Answer the following questions:[br]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.)[br]b) What is significant about the roots of the derivative? [br]c) Is there anything else you can say about how the graph of the derivative relates to the red graph?[br][br]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.[br]a) What is significant about the roots of the 2nd derivative?[br]b) What else can you say about how the graph of the 2nd derivative relates to the graph of the function?[br][br]Make as many generalizations as you can about the 1st and 2nd derivative.