Identify the Open Intervals Where the Function $f ( x ) = x \sqrt { 30 - x ^ { 2 } }$

question 123

Multiple Choice

Identify the open intervals where the function $f ( x ) = x \sqrt { 30 - x ^ { 2 } }$
is increasing or decreasing.

• A) decreasing: \(( - \infty , \sqrt { 15 } )\); increasing: \(( \sqrt { 15 } , \infty )\)
• B) decreasing on \(( - \infty , \infty )\)
• C) increasing: \(( - \infty , \sqrt { 30 } )\); decreasing: \(( \sqrt { 30 } , \infty )\)
• D) increasing: \(( - \sqrt { 15 } , \sqrt { 15 } ) ;\) decreasing: \(( - \sqrt { 30 } , - \sqrt { 15 } ) \cup ( \sqrt { 15 } , \sqrt { 30 } )\)
• E) increasing: \(( - \sqrt { 30 } , \sqrt { 15 } ) \cup ( \sqrt { 15 } , \sqrt { 30 } ) ;\) decreasing: \(( - \sqrt { 15 } , \sqrt { 15 } )\)

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