A curve can represent motion or change of some quantity such as distance. It is useful to find the rate of change of the curve or quantity. One way to find the rate of change is to draw a line through two points on the curve. Then the slope of that line is the average rate of change between the two points.[br][br]In this applet the small black points can be used to change the function curve. The orange points can be moved along the curve and the average rate of change between the points is calculated and displayed.

Note how the rate of change varies as[br][list=1][br][*]You switch point [math]2[/math] and point [math]1[/math].[br][*]You move the points closer together.[br][*]You put the points at the same location ( the points snap to the vertical grid lines )[br][/list][br][br]Where would you say the rate of change of the line is the same as the rate of change of the curve?