Use Lagrange Multipliers to Find the Given Extremum $x , y,$

question 23

Multiple Choice

Use Lagrange multipliers to find the given extremum. In each case, assume that $x , y,$ and $z$ are positive. Maximize $f ( x , y , z ) = x + y + z$ Constraints $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$

• A) \(f \left( \frac { \sqrt { 2 } } { 3 } , \frac { \sqrt { 2 } } { 3 } , \frac { \sqrt { 2 } } { 3 } \right) = \sqrt { 2 }\)
• B) \(f \left( \frac { \sqrt { 5 } } { 3 } , \frac { \sqrt { 5 } } { 3 } , \frac { \sqrt { 5 } } { 3 } \right) = \sqrt { 5 }\)
• C) \(f \left( \frac { \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } \right) = \sqrt { 3 }\)
• D) \(f ( \sqrt { 3 } , \sqrt { 3 } , \sqrt { 3 } ) = 3 \sqrt { 3 }\)
• E) \(f \left( \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } \right) = \sqrt { 3 }\)

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