Constructing Graphs of Derivative Functions (Intuitively)

In the following applet, the graph of a function is shown (in blue). You'll also notice there are 9 red points. The y-coordinate of each red point is the slope of the black line displayed either directly above or below it (or in some cases, directly on it). Your job is to move these 9 red points up and/or down so that ALL the black lines APPEAR TANGENT to the graph of the blue function. This exercise was designed to help you better intuitively understand how one can, given an original function, construct the graph of the derivative function. After completing each exercise, check the "Show Graph of Derivative Function" checkbox to see how you did. Click on the "Generate New Graph" button as many times as you need to practice this exercise.