The rate of change of most functions varies from point to point. [br]One can find out how the function f(x) changes by comparing it to the same function displaced a bit, say Δx.[br]The difference function Δf = f(x + Δx) - f(x) gives us a rough sense of how the function varies from point to point.[br][br]This rough sense is refined by making the displacement smaller. The trouble is that the difference[br]function gets smaller and smaller as the displacement gets smaller and smaller. [br][br]The situation can be saved by dividing the shrinking difference function by something else that is[br]shrinking at the same time, the value of the displacement Δx.[br][br]This environment allows you to explore this issue for several different type of functions. [br][br]Challenge:[br][br]Why does a WARNING! appear on the screen when the function Δf / Δx is displayed?