Determine the average rate of change for the following function over the given interval:
$\displaystyle
f(x)=x^2
$ between 3 and 9
The average rate of change is the following:
$\displaystyle f(x) \ = \ x^2 $
We get $\displaystyle f(3) \ = \ 9 $ and $\displaystyle f(9) \ = \ 81 $
What´s the difference between 81 and 9?
$\displaystyle 81 - 9 = 72 $
How many "steps" have we moved on the x-axis? We have moved
$\displaystyle 9 - 3 = 6 \ \mbox{steps} $
The average rate of change becomes $\displaystyle \frac{72}{6} \ = 12 $