Question

I keep getting the wring answer. Can you help?Find the average rate of change of each function on the interval specified. Answer in simplified factor form.

Answer 1

The first step is to evaluate the function at the extreme values of the interval:

$\begin{gathered} a(9)=\frac{1}{9+4}=\frac{1}{13} \\ a(9+h)=\frac{1}{9+h+4}=\frac{1}{13+h} \end{gathered}$

Now, find the difference between these values:

$\frac{1}{13+h}-\frac{1}{13}=\frac{13-(13+h)}{13(13+h)}=\frac{-h}{169+13h}$

Divide this difference by the difference of the extreme values:

$m=\frac{\frac{-h}{169+13h}}{9-(9+h)}=\frac{\frac{-h}{169+13h}}{-h}=\frac{-h}{-h(169+13h)}=\frac{1}{169+13h}$

It means that the rate of change of the interval is:

$\frac{1}{169+13h}=\frac{1}{13(13+h)}$