Average and Instantaneous Rates of Change of a Function

This applet illustrates the geometric interpretation of the average and instantaneous rates of change of a function s = f(x), where x measures time and s measures distance.
Drag the points P and Q to measure the average rate of change of the function f between the two points. Fix point P and move point Q towards P and try to estimate the limiting value of the average rate as Q gets closer and closer to P. What happens when P = Q?