# Math Help - Rate of change?

1. ## Rate of change?

Whats the average rate of change between x=6 and x=-6 for
f(x)=8x^2+1x+10

Are you waiting for a formula?

Find the average rate of change between $x=\text{-}6$ and $x=6$ for $f(x)\:=\:8x^2+1x+10$

$\begin{array}{cccccc}\text{When }x=\text{-}6\!: &f(\text{-}6) &=& 8(\text{-}6)^2 + (\text{-}6) + 10 &=& 292 \\
\text{When }x = 6\!: & f(6) &=& 8(6^2) + 6 + 10 &=& 304\end{array}$

The function changed by: $f(6) - f(\text{-}6) \:=\:304 - 292 \:=\:+12$ units
. . over a distance of: $6 - (\text{-}6) \:=\:12$ units.

Therefore, the average rate of change is: . $\frac{12}{12} \:=\:1$

3. if you are still waiting ...

the average rate of change for the function f over the interval [a,b] is

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