Consider the following nonconvex programming problem.
Maximize f(x) = x3 – 60x2 + 900x + 100,
subject to 0 ≤ x ≤ 31.
(a) Use the first and second derivatives of f(x) to determine the critical points (along with the end points of the feasible region) where x is either a local maximum or a local minimum.
(b) Roughly plot the graph of f(x) by hand over the feasible region.