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Find the Maximum and Minimum Values of the Function f(x,y)=xyf ( x , y ) = x y

Question 162

Essay

Find the maximum and minimum values of the function f(x,y)=xyf ( x , y ) = x y on the ellipse given by the equation x2+y24=1x ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1 .

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