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

Short Answer

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.