Consider the following convex programming problem:

Minimize Z x4 x2  4x, subject to x 2 and x  0.

(a) Use one simple calculation just to check whether the optimal solution lies in the interval 0 x 1 or the interval 1 x 2. (Do not actually solve for the optimal solution in order to determine in which interval it must lie.) Explain your logic.

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(b) Use the one-dimensional search procedure with initial bounds x 0, x 2 and with an error tolerance  0.02 to interactively solve (approximately) this problem.