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# Help

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Find the maximum value of $$f(x,y) = x \sqrt{1 - y^2} + y \sqrt{1 - x^2},$$where $$-1 \le x, y \le 1.$$

Aug 10, 2019

#1
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Hint:

Because this is symmetric with respect to x and y, the maximum (and minimum) will occur when x = y.

Hence find the maximum of $$2x\sqrt{1-x^2}$$

Aug 11, 2019