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

question 123

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:

Mean

Calculating the average involves summing all numbers in a set and then dividing by the quantity of those numbers.

Probability Distribution

A mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

Variance

A measure of the spread of a set of data points around their mean value, indicating how much the data varies.

Binomial Random Variable

A type of random variable that results from an experiment consisting of a fixed number of independent trials, each with two possible outcomes (success or failure).