Answer
(a) $5h^{2}+30h$
(b) $5h+30$
Work Step by Step
We are given: $f(t)=5t^2$; $t=3$, $t=3+h$
(a) We calculate the net change:
$f(3+h)-f(3)=[5(3+h)^{2}]-[5(3)^{2}]=45+30h+5h^{2}-45=5h^{2}+30h$
(b) We calculate the average rate of change:
$\displaystyle \frac{f(3+h)-f(3)}{(3+h)-3}=\frac{5h^{2}+30h}{h}=\frac{h(5h+30)}{h}=5h+30$
