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

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: $( - \sqrt { 15 } , \sqrt { 15 } )$