Problem 2. Consider the minimization problem f(x) = (x1x₂ + 2)² + (p − 1)(x² + 2x₁ + x² - 4x₂), where x = (₁, ₂), p = R. Answer the

following questions, and justify your answers rigorously. (a) There is a point x = (x,x) such that x* is a stationary point for any p. Find such a x*. (5 marks) (5 (b) For which value(s) of p does x* satisfy the second-order necessary condition? marks) (c) For which value(s) of p does x* satisfy the second-order sufficient condition? marks) (d) For which value(s) of p, would f is convex in a neighborhood of x*? (5 (5 marks)