Solve the Problem $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$

question 250

Multiple Choice

Solve the problem.
-Find the extreme values of $f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ subject to $3 x - y + z = 6$ and $x + 2 y + 2 z = 2$ .

• A) Maximum: none; minimum: \(\frac { 148 } { 45 }\) at \(\left( - \frac { 74 } { 45 } , \frac { 20 } { 45 } , \frac { 28 } { 45 } \right)\)
• B) Maximum: none; minimum: \(\frac { 148 } { 45 }\) at \(\left\{ \frac { 74 } { 45 } , \frac { 20 } { 45 } , - \frac { 28 } { 45 } \right)\)
• C) Maximum: none; minimum: \(\frac { 148 } { 45 }\) at \(\left\{ \frac { 74 } { 45 } , - \frac { 20 } { 45 } , \frac { 28 } { 45 } \right)\)
• D) Maximum: none; minimum: \(\frac { 148 } { 45 }\) at \(\left\{ \frac { 74 } { 45 } , - \frac { 20 } { 45 } , - \frac { 28 } { 45 } \right)\)

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