# How do you calculate rate of change?

Nov 13, 2014

Average Rate of Change

The average rate of change of a function $f \left(x\right)$ on an interval $\left[a , b\right]$ can be found by

$\left(\text{Average Rate of Change}\right) = \frac{f \left(b\right) - f \left(a\right)}{b - a}$

Example

Find the average rate of change of $f \left(x\right) = {x}^{2} + 3 x$ on $\left[1 , 3\right]$.

$f \left(3\right) = {\left(3\right)}^{2} + 3 \left(3\right) = 18$

$f \left(1\right) = {\left(1\right)}^{2} + 3 \left(1\right) = 4$

$\left(\text{Average Rate of Change}\right) = \frac{f \left(3\right) - f \left(1\right)}{3 - 1} = \frac{18 - 4}{2} = \frac{14}{2} = 7$

I hope that this was helpful.