Let $f ( x , y , z ) = x ^ { 2 } + 4 y ^ { 2 } + 16 z ^ { 2 }$

Multiple Choice

Let $f ( x , y , z ) = x ^ { 2 } + 4 y ^ { 2 } + 16 z ^ { 2 }$ with constraint xy = 1. Then f has a relative minimum at

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