A particle moves according to a law of motion s = f(t), t 0, where t is measured in seconds and s in feet.

f(t) = t³ 12t² + 36t

(a) Find the velocity at time t.

(b) What is the velocity after 5 s?

(c) When, for 0 t < , is the particle speeding up? (Enter your answer in interval notation.)

(d) When, for 0 t < , is it slowing down? (Enter your answer in interval notation.)