solution

Find the critical values of the following functions. Also determine the optima, if they exist.

(i) U = f (x,y) = 10 + x2 + y2 − 4x − 4y; (ii) U = f (x, y) = 10 − x2 − y210x + 10y; (iii) U = f (x,y) = x3 +y3 −xy; (iv) U = f (x, y) = x3 +y3 −9x −9y; (v) U = f (x,y) = x2 − 4xy − y2; (vi) U = f (x,y) = x2 + 2xy + y3; (vii) U = f (x,y) = x3 − xy + y3; (viii) U = f (x,y) = xy − x3 − y3.

 
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