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

Apr 18, 2016

7

#### Explanation:

The average rate of change is found using

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{f \left(b\right) - f \left(a\right)}{b - a}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In the interval [1 , 2 ] , a = 1 and b = 2 ( from left to right )

$\Rightarrow \frac{f \left(2\right) - f \left(1\right)}{2 - 1} \text{ is required to be calculated }$

f(2) $= 3 {\left(2\right)}^{2} - 2 \left(2\right) = 8$

and f(1) =3 - 2 = 1

$\Rightarrow \text{ average rate of change } = \frac{8 - 1}{1} = 7$