Question

Find the average rate of change of each function on the interval specified in simplest form. Do not type your answer in factored form and do not type any spaces between characters. k(x)=4x-2 on the interval [3,3+h]The average rate of change is Answer

Answer 1

Given the function:

`k(x)=4x-2`

The average rate of change is given by the formula:

`(k(a)-k(b))/(a-b)`

The given function on the interval [3, 3+h]

So, we will find k(3) and k(3+h) as follows:

`\begin{gathered} k(3)=4\cdot3-2=12-2=10 \\ k(3+h)=4\cdot(3+h)-2=12+4h-2=4h-10 \end{gathered}`

the average rate of change will be:

`(k(3+h)-k(3))/((3+h)-(3))=((4h+10)-(10))/((3+h)-(3))=(4h+10-10)/(3+h-3)=(4h)/(h)=4`

so, the answer will be the average rate of change = 4