Let $f ( x , y ) = x y$ With Constraint

Multiple Choice

Let $f ( x , y ) = x y$ with constraint $3 x ^ { 2 } + y ^ { 2 } = 6$ . Then f has a relative minimum at

A) $( 1 , \sqrt { 3 } )$
B) $( - 1 , \sqrt { 3 } )$
C) $( 1 , - \sqrt { 3 } )$
D) $( \pm 1 , \pm \sqrt { 3 } ) ( \pm 1 , \mp \sqrt { 3 } )$
E) $( \pm 1 , \mp \sqrt { 3 } )$