Solve the Problem $f ( x , y , z ) = 2 x - 3 y + z$

question 386

Multiple Choice

Solve the problem.
-Find the extreme values of $f ( x , y , z ) = 2 x - 3 y + z$ subject to $x ^ { 2 } + y ^ { 2 } = 1$ and $y ^ { 2 } + z ^ { 2 } = 1$ .

• A) Maximum: \(3 \sqrt { 2 }\) at \(\left( \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right) ;\) minimum: \(- 3 \sqrt { 2 }\) at \(\left( - \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } \right)\)
• B) Maximum: \(2 \sqrt { 2 }\) at \(\left( \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } \right) ;\) minimum: \(- 2 \sqrt { 2 }\) at \(\left( - \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right)\)
• C) Maximum: \(\sqrt { 2 }\) at \(\left( - \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right) ;\) minimum: \(- \sqrt { 2 }\) at \(\left( \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } \right)\)
• D) Maximum: \(4 \sqrt { 2 }\) at \(\left( \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right) ;\) minimum: \(- 4 \sqrt { 2 }\) at \(\left( - \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } , - \frac { 1 } { \sqrt { 2 } } \right)\)

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Definitions:

Sensation-Type

This term appears to relate to psychological typologies, possibly referring to a preference for sensory input and practical experiences in decision-making processes.

Problem-Solving Styles

The various approaches or strategies individuals employ when confronting and resolving issues or challenges.

Sensation-Type

A personality dimension focusing on individuals who prefer concrete, practical information and experiences.

Routine And Order

The structured and predictable pattern of activities or procedures that facilitate the smooth operation of an organization or daily life.