Average Rate of Change of a Function: Dynamic Illustration

The average rate of change of a continuous function f from input value x = a to input value x = b is given by . The applet below provides a dynamic visual interpretation of this expression. Interact with this applet for a few minutes. You can input different functions in the input box in the upper right-hand corner. You can also adjust the input values a and b using the sliders or their respective input boxes. Please answer the question that follows.


Given what you saw in the applet above, how can the expression be interpreted geometrically? That is, can you provide an alternate way to describe what you're finding when you algebraically evaluate the expression ?