Question

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

Answer 1

Given the function:

`j(x)=3x^3`

We will find the average rate of change of each function on the interval

`\lbrack1,1+h\rbrack`

The average rate of change of the function will be given by:

`(j(1+h)-j(1))/((1+h)-1)`

So, first, we will calculate j(1+h) and j(1)

`\begin{gathered} j(1)=3\cdot(1)^3=3 \\ j(1+h)=3(1+h)^3=3(1+3h+3h^2+h^3) \\ j(1+h)=3+9h+9h^2+3h^3 \end{gathered}`

So, the average rate will be:

`((3+9h+9h^2+3h^3)-3)/(1+h-1)=(9h+9h^2+3h^3)/(h)=9+9h+3h^2`

So, the answer will be:

`3h^2+9h+9`