Determine the X-Coordinate(s) of Any Relative Extrema and Inflection Points $y = x ^ { 5 } \ln \frac { x } { 9 }$

question 85

Multiple Choice

Determine the x-coordinate(s) of any relative extrema and inflection points of the function $y = x ^ { 5 } \ln \frac { x } { 9 }$

• A)relative minimum: \(x = 9 e ^ { \frac { - 1 } { 5 } }\); no inflection points
• B)relative maximum: \(x = 9 e ^ { \frac { - 1 } { 5 } } ;\) inflection point: \(x = 9 e ^ { \frac { - 9 } { 20 } }\)
• C)no relative maximum or minimum; inflection point: \(x = 9 e ^ { \frac { - 1 } { 5 } }\)
• D) no relative extrema or inflection points.
• E)relative minimum: \(x = 9 e ^ { \frac { - 1 } { 5 } } ;\) inflection point: \(x = 9 e ^ { \frac { - 9 } { 20 } }\)

---

Definitions:

Interpretation

The process of providing meaning or explanation for something, often used in the analysis of data or in the understanding of human behavior.

Infantile Veneer

A concept suggesting that adult behavior and emotions are sometimes overlays covering unresolved childhood conflicts.

Psychoanalysis

A therapeutic approach developed by Sigmund Freud focusing on unconscious processes as they are manifested in an individual's behavior, emphasizing the exploration of dreams, fantasies, and free association.

Anna Freud

An influential psychoanalyst known for her work on defense mechanisms, ego psychology, and child psychoanalysis; daughter of Sigmund Freud.