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

question 26

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

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