Provide an Appropriate Response $t$ Corresponding to the Extrema Of $f ( x , y , z ) = \sin \left( x ^ { 2 } + y ^ { 2 } \right) \cos ( z )$

question 243

Multiple Choice

Provide an appropriate response.
-Find the value(s) of $t$ corresponding to the extrema of $f ( x , y , z ) = \sin \left( x ^ { 2 } + y ^ { 2 } \right) \cos ( z )$ subject to the constraints $x ^ { 2 } +$ $y ^ { 2 } = 6 t , 0 \leq t \leq \pi$ , and $z = \frac { \pi } { 6 }$ . Classify each extremum as a minimum or maximum. (Hint: $w = f ( x , y , z )$ is a differentiable function of t.

• A) \(t = \frac { \pi } { 12 }\), minimum; \(t = 0\), maximum
• B) \(t = \frac { \pi } { 12 }\), minimum
• C) \( \mathrm { t } = - \frac { \pi } { 12 }\), maximum
• D) \(\mathrm { t } = \frac { \pi } { 12 }\), minimum; \(\mathrm { t } = - \frac { \pi } { 12 }\), maximum

---

Definitions:

Coercive Leader

A leadership style characterized by the use of threats, punishment, and control to influence the behavior of followers.

Trait Viewpoint

A perspective in leadership theory that suggests certain inherent personality traits and characteristics can make an individual a good leader.

Process

A series of actions or steps taken in order to achieve a particular end.

Management

The process of dealing with or controlling things or people, often within an organization.