# How do you find the average rate of change of f(x)=-3x^2+2 between [0,3]?

May 5, 2018

Average rate of change$= - 9$

#### Explanation:

The average rate of change is denoted by this formula

$\frac{f \left({x}_{a}\right) - f \left({x}_{b}\right)}{a - b}$

Let $a = 3$ and $b = 0$,

$\frac{f \left(3\right) - f \left(0\right)}{3 - 0}$

Expand,

$\frac{\left(- 3 {\left(3\right)}^{2} + 2\right) - \left(- 3 {\left(0\right)}^{2} + 2\right)}{3}$

Simplify,

$\frac{- 25 - 2}{3}$

Solve,

$- 9$