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

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