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)=(1)/(9+4)=(1)/(13) \\ a(9+h)=(1)/(9+h+4)=(1)/(13+h) \end{gathered}`

Now, find the difference between these values:

`(1)/(13+h)-(1)/(13)=(13-(13+h))/(13(13+h))=(-h)/(169+13h)`

Divide this difference by the difference of the extreme values:

`m=((-h)/(169+13h))/(9-(9+h))=((-h)/(169+13h))/(-h)=(-h)/(-h(169+13h))=(1)/(169+13h)`

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

`(1)/(169+13h)=(1)/(13(13+h))`