# How do you find the average rate of change of (x) = 3x^2 + 1 over [1,4]?

Jan 3, 2016

15

#### Explanation:

the average rate of change is the slope

slope = $\frac{\Delta y}{\Delta x}$

= (f(4) - f(1)) / (x_2 -x_1

f(4) = $3 {\left(4\right)}^{2} + 1 = 48 + 1 = 49$
f(1) = $3 {\left(1\right)}^{2} + 1 = 3 + 1 = 4$

so slope = $\frac{49 - 4}{4 - 1}$ = $\frac{45}{3}$ = 15