Locate Any Relative Extrema and Inflection Points of the Function $y = x \ln \frac { x ^ { 9 } } { 8 }$

question 59

Multiple Choice

Locate any relative extrema and inflection points of the function $y = x \ln \frac { x ^ { 9 } } { 8 }$ .

• A)no relative extrema; inflection point at \(x = 8 e ^ { \frac { - 17 } { 72 } }\)
• B)relative maximum at \(x = \left( \frac { 8 } { e } \right) ^ { \frac { 1 } { 9 } }\) ; inflection point at \(x = 8 e ^ { \frac { - 1 } { 9 } }\)
• C)relative minimum at \(x = 8 e ^ { \frac { 1 } { 9 } }\) ; inflection point at \(x = 8 e ^ { \frac { - 17 } { 72 } }\)
• D)no relative extrema; inflection point at \(x = 8 e ^ { \frac { - 17 } { 72 } }\)
• E)relative minimum at \(x = \left( \frac { 8 } { e } \right) ^ { \frac { 1 } { 9 } }\) ; no inflection points

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Definitions:

Humanistic Therapy

A form of psychotherapy that emphasizes personal growth and the achievement of maximum potential by focusing on the individual's unique self and subjective experience.

Psychological Problems

Mental or behavioral patterns that can cause significant distress or impairment in personal functioning.

Optimal Level

The most favorable or advantageous degree of intensity or concentration for a specific function or activity.

Transference

A phenomenon in psychoanalysis where patients project feelings, attitudes, or desires onto their therapist, confusing the therapist with figures from their past.