Chapter 13 - Section 13.3 - Tangent Lines and Derivatives - 13.3 Exercises - Page 921: 2

$\frac{f(x)-f(a)}{x-a}$. $instantaneous$ $f'(a)$.

If $y=f(x)$, the average rate of change of $f$ between the numbers $x$ and $a$ is $\frac{f(x)-f(a)}{x-a}$. The limit of the average rates of change as $x$ approaches $a$ is the $instantaneous$ rate of change of $y$ with respect to $x$ at $x=a$; this is also the derivative $f'(a)$.