Let $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 3 x + 4$

Multiple Choice

Let $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 3 x + 4$ Then which of the following is the largest interval, of those listed, for which $f ^ { \prime } ( x ) > 0$ for all x in that interval?

A) $( - \infty , \infty )$
B) $( - \infty , - 3 )$
C) $( - \infty , 3 )$
D) (-3,3)
E) $( 3 , \infty )$