# How do you find the average rate of change of f(x)=6x^2+1 over points (2, 25) and (3, 55)?

Jul 3, 2018

Average rate of change $= \frac{30}{1}$

#### Explanation:

Given: $f \left(x\right) = 6 {x}^{2} + 1$. Find the average rate of change from $\left(2 , 25\right)$ and $\left(3 , 55\right)$.

The average rate of change for a linear function is it's slope. When the function is not linear, the average rate of change is the slope between the two points.

Average rate of change $= \frac{f \left(b\right) - f \left(a\right)}{b - a}$

Let a = 2 => f(a) = 25; " "b = 3 => f(b) = 55

Average rate of change $= \frac{55 - 25}{3 - 2} = \frac{30}{1}$