Question: Show that (x, y) = x 2 has infinitely many critical points (as a function of two variables) and that the Second Derivative Test fails

Show that ƒ(x, y) = x² has infinitely many critical points (as a function of two variables) and that the Second Derivative Test fails for all of them. What is the minimum value of ƒ? Does ƒ(x, y) have any local maxima?

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