# Question: Consider the following nonconvex programming problem Maximize f x x3

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.

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.

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