# How do you find the average rate of change of f(x)=x^2+2 over [-2,1]?

Oct 13, 2015

$- \frac{2}{3}$

#### Explanation:

This is equivalent to asking for the average slope of the function between the 2 endpoints.

So we can find the function values at the 2 endpoints and then join the 2 and find the gradient of the straight line joining them.

$f \left(- 2\right) = {\left(- 2\right)}^{2} + 2 = 6$
$f \left(1\right) = {1}^{2} + 2 = 3$

Thus gradient $m = \frac{\Delta y}{\Delta x} = \frac{3 - 6}{1 - \left(- 2\right)} = - \frac{2}{3}$