Identify the Open Intervals Where the Function $f ( x ) = x \sqrt { 24 - x ^ { 2 } }$

question 75

Multiple Choice

Identify the open intervals where the function $f ( x ) = x \sqrt { 24 - x ^ { 2 } }$ is increasing or decreasing.

• A)decreasing: \(( - \infty , \sqrt { 12 } )\) ; increasing: \(( \sqrt { 12 } , \infty )\)
• B)increasing: \(( - \sqrt { 12 } , \sqrt { 12 } )\) ; decreasing: \(( - \sqrt { 24 } , - \sqrt { 12 } ) \cup ( \sqrt { 12 } , \sqrt { 24 } )\)
• C)increasing: \(( - \infty , \sqrt { 24 } )\) ; decreasing: \(( \sqrt { 24 } , \infty )\)
• D)increasing: \(( - \sqrt { 24 } , - \sqrt { 12 } ) \cup ( \sqrt { 12 } , \sqrt { 24 } )\) ; decreasing: \(( - \sqrt { 12 } , \sqrt { 12 } )\)
• E)decreasing for all x

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