Solve the Problem $z = 2 - x ^ { 2 } - y ^ { 2 }$

question 55

Multiple Choice

Solve the problem.
-Find the point on the paraboloid $z = 2 - x ^ { 2 } - y ^ { 2 }$ that is closest to the point $( 1,1,2 )$ .

• A) \(\left( - \frac { 1 } { 2 } , - \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)\)
• B) \(\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)\)
• C) \(\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)\)
• D) \(\left( \frac { 1 } { 2 } , - \frac { 1 } { 2 } , \frac { 3 } { 2 } \right)\)

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Definitions:

Conscientiousness

A characteristic of being well-organized, reliable, and having a deep commitment to responsibilities.

Emotional Stability

The ability of an individual to remain calm and composed under stress, showing resilience and consistency in emotional reactions.

Emotional Stability

refers to an individual's ability to remain calm and composed, managing their emotions effectively, especially in stressful situations.

Emotional Control

The ability to manage and regulate one's emotional responses to situations in a healthy and productive manner.