A 5-Year Projection of Population Trends Suggests That T Years $P ( t ) = - t ^ { 3 } + 12 t ^ { 2 } + 144 t + 50$

Short Answer

A 5-year projection of population trends suggests that t years from now, the population of a certain community will be $P ( t ) = - t ^ { 3 } + 12 t ^ { 2 } + 144 t + 50$ thousand.
a. At what time during the 5-year period will the population be growing most rapidly?
b. At what time during the 5-year period will the population be growing least rapidly?
c. At what time is the rate of population growth changing most rapidly?