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DEFINITION
The average rate of change of a
function $\,f\,$ from $\,a\,$ to $\,b\,$ is:
Given a function $f(x)$ the line that passes through two points
$(a,f(a))$ and $(b,f(b))$ is called the secant
line. $\displaystyle \frac{f(b)-f(a)}{b-a}$ The slope of the secant line is $\displaystyle \frac{f(b)-f(a)}{b-a}$ Thus, the slope of the secant line is also the average rate of change of the function. Let's explore this notion of average rate of change and secant lines using the applet below: Drag point b towards a to see the limiting behavior of the secant line. |