Chapter 12.2, Problem 68E

Prison Population The prison population in the United States can be approximated by

$N\left(t\right)=0.02t^3-2t^2+100t+1,100\text{ thousand people }\left(0\le t\le 18\right).$

(t is the year since 1990.) When, to the nearest year, was the prison population increasing most rapidly? When was it increasing least rapidly? [HINT: You are being asked to find the extreme values of the rate of change of the prison population.]