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Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant....

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Basic Math

Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The point (0,0) is a stationary point of f. For what values of k will f have alocal minimum at (0, 0)?

(a) |k| > 4

(b) k ≥ −4

(c) k ≤ 4

(d) |k| < 4

(e) none of the above

The point P : (2, 2) is a stationary point of the function f(x,y) = 6xy − x ^3 − y^ 3 . f has (a) a local maximum at P (b) a localminimum at P (c) a saddle point at P (d) a discontinuity at P (e)none of the above

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