Find the Exact Location of All the Relative and Absolute $( 0 , \infty )$

Multiple Choice

Find the exact location of all the relative and absolute extrema of the function with domain $( 0 , \infty )$ . $f ( x ) = x \ln \left( x ^ { 3 } \right)$

A) $\left( \frac { 1 } { e } , \frac { 3 } { e } \right)$ - absolute minimum
B) $\left( \frac { 1 } { e } , - \frac { 3 } { e } \right)$ - relative maximum
C) $\left( \frac { 3 } { e } , - \frac { 1 } { 3 e } \right)$ - absolute minimum
D) $\left( \frac { 1 } { e } , - \frac { 1 } { 3 e } \right)$ - relative minimum
E) $\left( \frac { 1 } { e } , - \frac { 3 } { e } \right)$ - absolute minimum