Analysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is

y = 70t + 0.5t² - t³, 0 ≤ t ≤ 8

(a) Find the critical values of this function.

(b) Which critical values make sense in this particular problem?

(c) For which values of t, for 0 ≤ t ≤ 8, is y increasing?

(d) Graph this function.