The first step is to evaluate the function at the extreme values of the interval:
[tex]\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}[/tex]
Now, find the difference between these values:
[tex]\frac{1}{13+h}-\frac{1}{13}=\frac{13-(13+h)}{13(13+h)}=\frac{-h}{169+13h}[/tex]
Divide this difference by the difference of the extreme values:
[tex]m=\frac{\frac{-h}{169+13h}}{9-(9+h)}=\frac{\frac{-h}{169+13h}}{-h}=\frac{-h}{-h(169+13h)}=\frac{1}{169+13h}[/tex]
It means that the rate of change of the interval is:
[tex]\frac{1}{169+13h}=\frac{1}{13(13+h)}[/tex]
