Determine the Nature of the Critical Points of the Function $f ( x , y ) = 3 x ^ { 5 } y + x y ^ { 5 } + x y$

Multiple Choice

Determine the nature of the critical points of the function $f ( x , y ) = 3 x ^ { 5 } y + x y ^ { 5 } + x y$

A) f has a saddle point at (1, 0) .
B) f has a local maximum at (0, 0) .
C) f has a saddle point at (0, 1) .
D) f has a saddle point at (0, 0) .
E) f has a local minimum at (0, 0) .