Find the Maximum Value of the Function $f ( x , y ) = x y$

question 36

Multiple Choice

Find the maximum value of the function $f ( x , y ) = x y$ subject to the constraint that $x ^ { 2 } + y ^ { 2 } = 2$ .

• A) \(\frac { 1 } { 2 }\)
• B)1
• C) \(\frac { 3 } { 2 }\)
• D)2
• E) \(- \frac { 1 } { 2 }\)
• F) \(- 1\)
• G) \(- \frac { 3 } { 2 }\)
• H) \(- 2\)

---

Definitions:

Disturbances of Thought

Any disruption or pathology in the process of thinking, such as disorganized thinking found in psychological disorders.

Emotional Reactions

The psychological and physiological responses that occur in response to stimuli that are personally significant.

Schizophrenic Patients

Individuals diagnosed with schizophrenia, a chronic brain disorder characterized by distorted thinking, perceptions, emotions, language, self-awareness, and behavior.

Blunted

A term often used in psychology to describe a reduced or muted emotional response to stimuli that typically evoke stronger reactions.