Question: 2. Consider the problem of minimizing (locally) the function ay) = 10(182 + yz 2w 2.7;) + (my 1)2, where :1: and y are real

2. Consider the problem of minimizing (locally) the function ay) = 10(182 + yz 2w 2.7;) + (my 1)2, where :1: and y are real numbers and p is a real parameter. Answer the following questions, justifying your answers rigorously. (a) What are values 930 and yo such that f has a stationary point at (930,310) for every value of p? (b) For which value(s) of 39 does (3:0, yo) satisfy the secondorder necessary condition? (0) For which value(s) of 3) does (3:0, yo) satisfy the second-order sufcient condition? ((1) For which value(s) of p can you be certain that f is convex in a neighborhood of ($0,310)

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