Answer
net change: $2h+h^2$
average rate of change: $2+h$
Work Step by Step
We are given:
$f(t)=t^2-2t$, $t=2$ to $t=2+h$
We find the net change over the interval given:
$f(2+h)-f(2)=[(2+h)^{2}-2(2+h)]-[2^{2}-2(2)]=(4+h^{2}+4h-4-2h)-(4-4)=2h+h^{2}$
We find the average rate of change over this interval:
$\displaystyle \frac{f(2+h)-f(2)}{2+h-2}=\frac{2h+h^{2}}{h}=\frac{h(2+h)}{h}=2+h$
