FUNCTIONS as OBJECTS: how they change - II

Functions as Objects - how they change [N.B. This applet is a more general version of an earlier applet with a nearly identical name. In this applet you can explore the global rate of change of any function of one variable that depends on up to three parameters] The rate of change of most functions varies from point to point. One can find out how the function f(x) changes by comparing it to the same function displaced a bit, say Δx. The difference function Δf = f(x + Δx) - f(x) gives us a rough sense of how the function varies from point to point. This rough sense is refined by making the displacement smaller. The trouble is that the difference function gets smaller and smaller as the displacement gets smaller and smaller. The situation can be saved by dividing the shrinking difference function by something else that is shrinking at the same time, i.e., the value of the displacement Δx. You can enter any function that depends of up to 3 parameters a,b, and c. Why does a WARNING! appear on the screen when the function Δf / Δx is displayed? What questions could/would you ask your students based on this applet?