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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

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