Find the Intervals Where $f ( x ) = \frac { \log 9 x } { x }$

question 27

Multiple Choice

Find the intervals where $f ( x ) = \frac { \log 9 x } { x }$ is increasing and where it is decreasing.

• A) increasing: \(( 9 e , \infty )\), decreasing: \(( 0,9 e )\)
• B) increasing: \(\left( 0 , \frac { e } { 9 } \right)\), decreasing: \(\left( \frac { e } { 9 } , \infty \right)\)
• C) increasing: \(( 90 , \infty )\), decreasing: \(( 0,90 )\)
• D) increasing: \(\left( 0 , \frac { 9 } { 10 } \right)\), decreasing: \(\left( \frac { 9 } { 10 } , \infty \right)\)

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Definitions:

Avolition

A symptom of various psychiatric disorders, characterized by a lack of motivation to initiate and complete tasks.

Long-term Amnesia

A significant loss of memory that extends over long periods, often resulting from brain injury or psychological trauma.

Schizophrenia

A chronic and severe mental disorder affecting how a person thinks, feels, and behaves, characterized by delusions, hallucinations, disorganized speech, and impaired cognitive function.

Religious Delusions

False beliefs that involve religious themes or content, often observed in individuals with psychotic disorders like schizophrenia.