Problem 1: Solve the problem of minimizing x2 - 4x + 1 subject to x4 – 1 ≤ 0.
Problem 2: Solve the problem of maximizing ƒ(x) = x subject to g(x) = x4 if x ≤ 0, 0 if x ? [0, 1], (x-1)4 if x ≥ 1. Explain why the Kuhn-Tucker conditions are in applicable in this case.