Find the Extreme Values of the Function Subject to the Given

question 52

Multiple Choice

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

• A) Maximum: none; minimum: \(\frac { 6 } { 11 }\) at \(\left( - \frac { 6 } { 11 } , \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)\)
• B) Maximum: none; minimum: \(\frac { 6 } { 11 }\) at \(\left. \} - \frac { 6 } { 11 } , - \frac { 3 } { 11 } , \frac { 2 } { 11 } \right)\)
• C) Maximum: none; minimum: \(\frac { 6 } { 11 }\) at \(\left\{ - \frac { 6 } { 11 } , - \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)\)
• D) Maximum: none; minimum: \(\frac { 6 } { 11 }\) at \(\left\{ \frac { 6 } { 11 } , - \frac { 3 } { 11 } , - \frac { 2 } { 11 } \right)\)

---

Definitions:

Trembling

Shaking or quivering movement, often resulting from nervousness, fear, excitement, or cold.

Electric Shock

A sudden discharge of electricity through a part of the human body, causing various effects from mild discomfort to serious injury or even death.

Development

The process of change and growth in humans or animals, which can be physical, cognitive, or social, from infancy through adulthood.

Phobias

Intense, irrational fears of specific objects or situations that significantly impair an individual's ability to function.