# Using the graph of f(x) = 2x^3 + x^2 - 3x+1, what is the average rate of change from x=-2 to x=0?

May 26, 2018

$3$

#### Explanation:

average rate of change on $x = - 2$ to $x = 0$ is:
$\frac{f \left(0\right) - f \left(- 2\right)}{0 - \left(- 2\right)}$
$= \frac{\left(2 {\left(0\right)}^{3} + {\left(0\right)}^{2} - 3 \left(0\right) + 1\right) - \left(2 {\left(- 2\right)}^{3} + {\left(- 2\right)}^{2} - 3 \left(- 2\right) + 1\right)}{2}$
$= \frac{1 - \left(- 5\right)}{2}$
$= 3$

graph{2x^3+x^2-3x+1 [-10, 10, -7, 7]}
the graph of $f \left(x\right)$ passes through points $\left(- 2 , - 5\right)$ and $\left(0 , 1\right)$

the slope of the line passing through those two points is the average rate of change.