Find the Absolute Maximum and Minimum Values of the Function $f ( x , y ) = x y ;$

question 335

Multiple Choice

Find the absolute maximum and minimum values of the function on the given curve.
-Function: $f ( x , y ) = x y ;$ curve: $x ^ { 2 } + y ^ { 2 } = 49 , x \geq 0 , y \geq 0$ . (Use the parametric equations $x = 7$ cos $t , y = 7 \sin t$ .)

• A) Absolute maximum: \(\frac { 49 } { 4 }\) at \(t = \frac { \pi } { 4 } ;\) absolute minimum: 0 at \(t = 0\) and \(t = \frac { \pi } { 2 }\)
• B) Absolute maximum: \(\frac { 49 } { 4 }\) at \(t = \frac { \pi } { 4 }\); absolute minimum: 0 at \(t = 0\) and \(t = \frac { \pi } { 4 }\)
• C) Absolute maximum: \(\frac { 49 } { 2 }\) at \(t = \frac { \pi } { 4 } ;\) absolute minimum: 0 at \(t = 0\) and \(t = \frac { \pi } { 2 }\)
• D) Absolute maximum: \(\frac { 49 } { 2 }\) at \(t = \frac { \pi } { 4 } ;\) absolute minimum: 0 at \(t = 0\) and \(t = \frac { \pi } { 4 }\)

Identify the locations and functions of taste receptors.

Comprehend the influence of biological, experiential, and cultural factors on the perception of pain.

Differentiate between the basic tastes and recognize the non-existence of a "bland" taste.

Learn about the body's natural pain management mechanisms, including the role of endorphins and the pain gate theory.

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Definitions:

Expectancy Theory

A motivational theory suggesting that an individual’s motivation is an outcome of how much an individual wants a reward, the assessment of the likelihood that the effort will lead to expected performance, and the belief that the performance will lead to a reward.

Equity Theory

A theory in social psychology that explains how individuals perceive fairness in the distribution of resources and rewards, influencing their motivation and satisfaction.

Goal-Setting Theory

An organizational framework positing that specific and challenging goals, along with appropriate feedback, facilitate improved worker performance.

Negative Reinforcement

Strengthens a behaviour by making the avoidance of an undesirable consequence contingent on its occurrence.