Derivative Function: Without Words

In the applet below, a function f is shown (black). Its derivative function, f', is shown in gray. Feel free to input any function you'd like. Slide the slider to see the physical meaning of the derivative of a function (at a certain input value: x-coordinate of white point) within this graphical context. How can we sketch the graph of the derivative of a function? Explain.

Quick Demo (BGM: Andy Hunter)