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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