Given the function:
[tex]k(x)=4x-2[/tex]
The average rate of change is given by the formula:
[tex]\frac{k(a)-k(b)}{a-b}[/tex]
The given function on the interval [3, 3+h]
So, we will find k(3) and k(3+h) as follows:
[tex]\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}[/tex]
the average rate of change will be:
[tex]\frac{k(3+h)-k(3)}{(3+h)-(3)}=\frac{(4h+10)-(10)}{(3+h)-(3)}=\frac{4h+10-10}{3+h-3}=\frac{4h}{h}=4[/tex]
so, the answer will be the average rate of change = 4
