Consider the function $f ( x , y ) = x ^ { 4 } + 2 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 3 } - y ^ { 4 } + 3$ Check that (0,0)is a critical point of f and classify it as a local minimum, local maximum or saddle point.

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The Answer of Consider the function $f ( x , y ) = x ^ { 4 } + 2 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 3 } - y ^ { 4 } + 3$ Check that (0,0)is a critical point of f and classify it as a local minimum, local maximum or saddle point.

Consider the Function f(x,y)=x4+2x3y−6x2y2+7xy3−y4+3f ( x , y ) = x ^ { 4 } + 2 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 3 } - y ^ { 4 } + 3f(x,y)=x4+2x3y−6x2y2+7xy3−y4+3

Consider the Function $f ( x , y ) = x ^ { 4 } + 2 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } + 7 x y ^ { 3 } - y ^ { 4 } + 3$