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:

$\frac{j(1+h)-j(1)}{(1+h)-1}$

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:

$\frac{(3+9h+9h^2+3h^3)-3}{1+h-1}=\frac{9h+9h^2+3h^3}{h}=9+9h+3h^2$

So, the answer will be:

$3h^2+9h+9$