2. For each of the following, find the maximum and minimum of f on H.

(a) f (x, y) = x2 + 2x - y2 and H = {(x, y) : x2 + 4y2 :::; 4}.

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(b) f (x, y) = x2 + 2xy + 3y2, and H is the region bounded by the triangle with vertices (1,0), (1,2), (3,0).

(c) f(x, y) = x3 + 3xy - y3, and H = [-1,1] x [-1,1].