A time study showed that, on average, the productivity of a worker after t hours on the job can be modeled by the equation:
P(t) = 21t + 6t^2 - t^3, 0 ≤ t ≤ 8
where P represents the number of units produced per hour.
(a) Find the critical values of this function. (Assume -∞ < t < ∞. Enter your answers as a comma-separated list.)
t =
(b) Which critical value makes sense in this model?
t =
(c) For what values of t, for 0 ≤ t ≤ 8, is P increasing? (Enter your answer using interval notation.)