Find the Extreme Values of the Function Subject to the Given

question 239

Multiple Choice

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

• A) Maximum: none; minimum: \(\frac { 72 } { 7 }\) at \(\left( \frac { 6 } { 7 } , \frac { 12 } { 7 } , \frac { 18 } { 7 } \right)\)
• B) Maximum: none; minimum: \(\frac { 2 } { 7 }\) at \(\left( \frac { 1 } { 7 } , \frac { 2 } { 7 } , \frac { 3 } { 7 } \right)\)
• C) Maximum: none; minimum: 2 at \(\left( \frac { 1 } { 7 } , \frac { 4 } { 7 } , \frac { 9 } { 7 } \right)\)
• D) Maximum: none; minimum: \(\frac { 18 } { 7 }\) at \(\left( \frac { 3 } { 7 } , \frac { 6 } { 7 } , \frac { 9 } { 7 } \right)\)

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