Local minimum

Please see the attached file for the fully formatted problems.

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 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?