Find the Extreme Values of the Function Subject to the Given

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y , z ) = x ^ { 2 } + 2 y ^ { 2 } + 3 z ^ { 2 } , x - y - z = 1$$

A) Maximum: none; minimum: $\frac { 6 } { 11 }$ at $\left( - \frac { 6 } { 11 } , \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)$
B) Maximum: none; minimum: $\frac { 6 } { 11 }$ at $\left. \} - \frac { 6 } { 11 } , - \frac { 3 } { 11 } , \frac { 2 } { 11 } \right)$
C) Maximum: none; minimum: $\frac { 6 } { 11 }$ at $\left\{ - \frac { 6 } { 11 } , - \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)$
D) Maximum: none; minimum: $\frac { 6 } { 11 }$ at $\left\{ \frac { 6 } { 11 } , - \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)$