Find the Local Maximum and Minimum Values and Saddle Points $f ( x , y ) = 4 x y - x ^ { 4 } - y ^ { 4 } + \frac { 1 } { 16 }$

Essay

Find the local maximum and minimum values and saddle points of the function $f ( x , y ) = 4 x y - x ^ { 4 } - y ^ { 4 } + \frac { 1 } { 16 }$ .