Find the Extreme Values of the Function Subject to the Given

question 347

Multiple Choice

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

• A) Maximum: 9 at (3, 3, 3); minimum: 3 at (1, 1, 1)
• B) Maximum: 11 at (6, 3, 2), (6, 2, 3), (3, 2, 6), (3, 6, 2), (2, 3, 6), (2, 6, 3); minimum: 1 at (1, 1, -1), (1, -1, 1), (-1, 1, 1)
• C) Maximum: 6 at (2, 2, 2); minimum: -3 at (-1, -1, -1)
• D) Maximum: 6 at (2, 2, 2); minimum: 3 at (1, 1, 1)

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