Use the derivative to determine whether f is increasing, decreasing, or both.

Here is a short sweet GeoGebra worksheet to help students see the connection between the graph of y = f'(x) and the location of intervals where f is increasing or decreasing.  The worksheet randomly generates 3rd-degree polynomial functions and displays the parabolic graphs of their derivatives.  Students then decide whether the unseen original function f is increasing everywhere, decreasing everywhere, or increasing on some intervals and decreasing on others.  It usually does not take long to exhaust the three possible cases which are presented here, but as an added bonus, one of course can emphasize that the real zeros of the derivative (if there are any) correspond to values where the relative extrema of the function f may occur.