Find the Extreme Values of the Function Subject to the Given

question 85

Multiple Choice

Find the extreme values of the function subject to the given constraint.
- $$f ( x , y ) = x y , \quad x ^ { 2 } + y ^ { 2 } = 32$$

• A) Maximum: 16 at (4, 4); minimum: -16 at (-4, -4)
• B) Maximum: 16 at (4, -4) and (-4, 4); minimum: -16 at (4, 4) and (-4, -4)
• C) Maximum: 16 at (4, 4) and (-4, -4); minimum: -16 at (4, -4) and (-4, 4)
• D) Maximum: 16 at (4, 4); minimum: 0 at (0, 0)

---

Definitions:

Night's Sleep

The period of restful sleep experienced during the night, essential for physical and mental health.

Psychoanalytic Theory

A theory of personality organization and the dynamics of personality development that guides psychoanalysis, developed by Sigmund Freud.

Dreaming

The experience of envisioned images, sounds, or other sensations during sleep, often narrative in nature and occurring in REM sleep.

Empirical Support

Evidence that is based on observation, experience, or experiment, rather than theory alone, used to validate a hypothesis or claim.