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:

Electrodes

Conductors through which electricity enters or leaves an object, substance, or region, often used in medical and research settings to measure electrical activity.

Nervous System

The complex network of nerves and cells that carries messages to and from the brain and spinal cord to various parts of the body.

Breathing

The physiological process of inhaling oxygen and exhaling carbon dioxide from the bloodstream through the respiratory system.

Heart Rate

Heart Rate is the number of heartbeats per unit of time, typically expressed as beats per minute (BPM), a key indicator of physical exertion and overall cardiovascular health.