Find All Points (X, Y) Where $f ( x , y ) = e ^ { \left( x ^ { 2 } + y ^ { 2 } \right) }$

Multiple Choice

Find all points (x, y) where $f ( x , y ) = e ^ { \left( x ^ { 2 } + y ^ { 2 } \right) }$ has a possible relative maximum or minimum. Use the second-derivative test to determine, if possible, the nature of f(x, y) at each of these points.

A) (0, 1) gives a relative minimum point
B) (0, 0) gives a relative minimum point
C) (0, 1) gives a relative maximum point
D) (0, 0) gives a relative maximum point