Let $f ( x ) = \sqrt { x } \ln x$

Multiple Choice

Let $f ( x ) = \sqrt { x } \ln x$ . Find the interval on which $f$ is increasing.

A) $( 0 , \infty )$
B) $( 0,1 ]$
C) $[ 1 , \infty )$
D) $\left( 0 , e ^ { - 1 } \right]$
E) $\left[ e ^ { - 1 } , \infty \right)$
F) $\left( 0 , e ^ { - 2 } \right]$
G) $\left[ e ^ { - 2 } , \infty \right)$
H) $( 0 , \sqrt { e } )$