Question: The profit P(t) for a firm as a function of time (t) is described by the equation
P(t) = t - (3/8) t^2 + 1/24t^3 for 0 ≤ t ≤ 10.
For 0 ≤ t ≤ 10 show that there is exactly one local minimum, and find the value of t at which it occurs. Is the profit positive at this local minimum?