Find the Open Intervals on Which the Function $f ( x ) = \frac { x } { x ^ { 2 } + 36 }$

question 13

Multiple Choice

Find the open intervals on which the function $f ( x ) = \frac { x } { x ^ { 2 } + 36 }$ is increasing or decreasing.

• A)The function is increasing on the interval \(- 6 < x < 6\) , and decreasing on the intervals \(- \infty < x < - 6\) and \(6 < x < \infty\) .
• B)The function is increasing on the interval \(- \infty < x < - 6\) , and decreasing on the intervals \(- 6 < x < 6\) and \(6 < x < \infty\) .
• C)The function is increasing on the interval \(6 < x < \infty\) , and decreasing on the intervals \(- \infty < x < - 6\) and \(- 6 < x < 6\) .
• D)The function is decreasing on the interval \(- 6 < x < 6\) , and increasing on the intervals \(- \infty < x < - 6\) and \(6 < x < \infty\) .
• E)The function is decreasing on the interval \(- \infty < x < - 6\) , and increasing on the intervals \(- 6 < x < 6\) and \(6 < x < \infty\) .

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Definitions:

Direct Materials Price

The cost per unit of raw materials that are directly traceable to the production of goods.

Direct Labor Rate Variances

The difference between the actual cost of direct labor and the expected (or standard) cost, used in variance analysis to monitor labor costs.

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Budgeted standards represent targeted financial goals or benchmarks that a company aims to achieve within a certain period, often used in performance assessment and planning.

Raw Material

Basic substances in their natural, modified, or unprocessed states, used in the production or manufacturing of goods.