# What is the difference between Average rate of change and instantaneous rate of change?

The average rate of change of a function $f \left(x\right)$ on an interval $\left[a , b\right]$ is the slope of the secant line, which can be found by
$\frac{f \left(b\right) - f \left(a\right)}{b - a}$,
and the instantaneous rate of change of $f \left(x\right)$ at $x = a$ is the slope of the tangent line, which can be found by
$f ' \left(a\right)$.