Find the Point at Which the Function $f ( x , y , z ) = 2 x + y - 2 z$

Multiple Choice

Find the point at which the function $f ( x , y , z ) = 2 x + y - 2 z$ has the minimum value subject to the constraint that $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ .

A) $\left( \frac { 4 } { 3 } , \frac { 2 } { 3 } , \frac { 4 } { 3 } \right)$

B) $\left( \frac { 4 } { 3 } , \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right)$
C) $\left( \frac { 4 } { 3 } , - \frac { 2 } { 3 } , \frac { 4 } { 3 } \right)$
D) $\left( \frac { 4 } { 3 } , - \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right)$
E) $\left( - \frac { 4 } { 3 } , - \frac { 2 } { 3 } , \frac { 4 } { 3 } \right)$
F) $\left( - \frac { 4 } { 3 } , - \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right)$

G) $\left( - \frac { 4 } { 3 } , \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right)$

H) None of these