# How do you find the average rate of change of y = 9x^3 - 2x2 + 6 over interval [-4,2]?

Jul 10, 2018

$112$

#### Explanation:

$\text{the average rate of change of y over a closed interval}$
$\left[a , b\right] \text{ is a measure of the slope of the secant connecting}$
$\text{the 2 points and is calculated using}$

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

$\text{here } \left[a , b\right] = \left[- 4 , 2\right]$

$f \left(b\right) = f \left(2\right) = 9 {\left(2\right)}^{3} - 2 {\left(2\right)}^{2} + 6$

$\textcolor{w h i t e}{\times \times \times \times} = 72 - 8 + 6 = 70$

$f \left(a\right) = f \left(- 4\right) = 9 {\left(- 4\right)}^{3} - 2 {\left(- 4\right)}^{2} + 6$

$\textcolor{w h i t e}{\times \times \times \times \times} = - 576 - 32 + 6 = - 602$

$\text{average rate of change } = \frac{70 - \left(- 602\right)}{2 - \left(- 4\right)}$

$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times} = \frac{672}{6} = 112$