A time study showed that, on average, the productivity of a worker after t hours on the

Question:

A time study showed that, on average, the productivity of a worker after t hours on the job
Can be modeled by p(t) = 27t + 6t2 - t3, 0 ≤ t ≤ 8
Where P is the number of units produced per hour.
(a) Find the critical values of this function.
(b) Which critical value makes sense in this model?
(c) For what values of t is P increasing?
(d) Graph the function for 0 ≤ t ≤ 8.