# How do you calculate the average rate of change of f(x) =x^2+3x-2 on the interval 1<=x<=4?

Dec 18, 2017

$\frac{13}{3}$

#### Explanation:

average rate of change is simply the slope of the line through $\left(1 , f \left(1\right)\right) \mathmr{and} \left(4 , f \left(4\right)\right)$

$f \left(1\right) = {1}^{2} + 3 \left(1\right) - 2 = 2$
$f \left(4\right) = {4}^{2} + 3 \left(4\right) - 2 = 26$

average rate of change: $\frac{26 - 2}{4 - 1} = \frac{13}{3}$