# Math Help - calculus:average rate of change

1. ## calculus:average rate of change

Determine the average rate of change for the following function over the given interval:
$

f(x)=x^2
$
between 3 and 9

2. ## hi

The average rate of change is the following:

$f(x) \ = \ x^2$

We get $f(3) \ = \ 9$ and $f(9) \ = \ 81$

What´s the difference between 81 and 9?
$81 - 9 = 72$

How many "steps" have we moved on the x-axis? We have moved
$9 - 3 = 6 \ \mbox{steps}$

The average rate of change becomes $\frac{72}{6} \ = 12$

3. The average rate of change is the slope of the secant line joining these two points.

$m_{secant} = \frac{f(9)-f(3)}{9-3} = \frac{81-9}{9-3} = \frac{72}{6} = 12$

4. ## hi

Chop Suey is also definetely correct, except $\frac{72}{6} = 12 \ \mbox{,not 13}$