Find the Extreme Values Of $f ( x , y ) = x y + 2 y ^ { 2 } + x ^ { 4 } - y ^ { 4 }$

question 227

Essay

Find the extreme values of $f ( x , y ) = x y + 2 y ^ { 2 } + x ^ { 4 } - y ^ { 4 }$ on the circle $x ^ { 2 } + y ^ { 2 } = 1$ .

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