Let $f ( x , y , z ) = x ^ { 2 } - y ^ { 2 }$

Multiple Choice

Let $f ( x , y , z ) = x ^ { 2 } - y ^ { 2 }$ with constraint $x ^ { 2 } + 2 y ^ { 2 } + 3 z ^ { 2 } = 1$ . Then f has a relative minimum at

A) $( \pm 1,0,0 )$
B) $( - 1,0,0 )$
C) $( 1,0,0 )$
D) $\left( \frac { 1 } { 2 } , 0 , \frac { 1 } { 2 } \right)$
E) $\left( \frac { 1 } { 2 } , 0 , - \frac { 1 } { 2 } \right)$