Show that f (x, y) = x 2 ye -x2-y 2 has maximum values at (1, 1/2)

Question:

Show that f (x, y) = x²ye^-x2-y² has maximum values at (±1, 1/√2) and minimum values at (±1, -1/√2). Show also that f has infinitely many other critical points and D = 0 at each of them. Which of them give rise to maximum values? Minimum values? Saddle points?

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