Answer
(a) -16
(b) -4
Work Step by Step
We are given: $g(t)=t^4-t^3+t^2$; $t=-2$, $t=2$
(a) We calculate the net change:
$g(2)-g(-2)=[2^{4}-2^{3}+2^{2}]-[(-2)^{4}-(-2)^{3}+(-2)^{2}]=12-28=(16-8+4)-(16--8+4)=-16$
(b) We calculate the average rate of change:
$\displaystyle \frac{g(2)-g(-2)}{2--2}=\frac{-16}{4}=-4$
