(a) Under what conditions on the constant k will the function
f (x,y) = kx2 − 2xy + ky2
have a nondegenerate local minimum at (0,0)? What about a local maximum?
(b) Under what conditions on the constant k will the function
have a nondegenerate local maximum at (0,0,0)? What about a nondegenerate local minimum?
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