# Average Rate of Change of a Function: Dynamic Illustration

- Author:
- Tim Brzezinski

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**Please answer the question that follows.*a*and*b*using the sliders or their respective input boxes.## 1.

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** ?