The Function $f ( x , y ) = x ^ { 2 } + y ^ { 2 } + x y$

Multiple Choice

The function $f ( x , y ) = x ^ { 2 } + y ^ { 2 } + x y$ has one critical point. Determine its location and type.

A) $( 2,1 )$ , saddle point
B) $( 2,1 )$ , minimum point
C) $( 2,1 )$ , maximum point
D) $( \sqrt { 2 } , 1 )$ , saddle point
E) $( \sqrt { 2 } , 1 )$ , minimum point
F) $( \sqrt { 2 } , 1 )$ , maximum point
G) $( 0,0 )$ , saddle point
H) $( 0,0 )$ , minimum point