The average rate of change of a continuous function [i]f[/i] from input value [i]x[/i] = [i]a[/i] to input value [i]x[/i] = [i]b[/i] is given by [math]f_{ave}=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/math]. [br][br]The applet below provides a dynamic visual interpretation of this expression. [br][br]Interact with this applet for a few minutes. [br][color=#444444][b]You can input different functions in the input box in the upper right-hand corner. [/b][/color][b]You can also adjust the input values [i]a[/i] and [i]b[/i] using the sliders or their respective input boxes. [br][/b][br]Please answer the question that follows.
Given what you saw in the applet above, [b]how can the expression [/b][math]f_{ave}=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/math][b] be interpreted geometrically? [/b] That is, [b]can you provide an alternate way to describe what you're finding when you algebraically evaluate the expression[/b] [math]f_{ave}=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/math] ?