Answer
(a) $-3h^{2}-12h$
(b) $-3h-12$
Work Step by Step
We are given: $f(x)=1-3x^2$; $x=2$, $x=2+h$
(a) We calculate the net change:
$f(2+h)-f(2)=[1-3(2+h)^{2}]-[1-3(2)^{2}]=[-3h^{2}-12h-11]-[-11]=-3h^{2}-12h$
(b) We calculate the average rate of change:
$\displaystyle \frac{f(2+h)-f(2)}{(2+h)-2}=\frac{-3h^{2}-12h}{h}=-3h-12$
