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{\bf Math 225 : Quiz\hfill Oct 16, 1991}

Show your work and circle your final answer.

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1. Find the maximum of $$f(x,y) = x^2 - x y + y^2 + 4$$ on the rectangle
$$-1 \le x \le 1,\qquad-1\le y \le 1$$
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2. Find the extreme values of $$f(x,y) = 2x - 3y$$ subject to the constraint
$$x^2 + 4y^2 = 4$$

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