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

Multiple Choice

Find the exact location of all the relative and absolute extrema of the function with domain $( - \infty , \infty )$ . $g ( x ) = \frac { 1 } { 4 } x ^ { 4 } - \frac { 2 } { 3 } x ^ { 3 } + \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 2 }$

A) $\left( 0 , \frac { 1 } { 5 } \right)$ - absolute maximum
B) $\left( 0 , \frac { 1 } { 5 } \right)$ - absolute minimum
C) $\left( 0 , \frac { 1 } { 3 } \right)$ - relative maximum
D) $\left( 0 , \frac { 1 } { 2 } \right)$ - absolute minimum
E) $( 0,1 )$ - relative maximum