Let a function $g : [ 0,4 ] \rightarrow R$ be defined as\\
$g ( x ) = \left\{ \begin{array} { c c } \max \left\{ t ^ { 3 } - 6 t ^ { 2 } + 9 t - 3 \right\} , & 0 \leq x \leq 3 \\ 0 \leq t \leq x & \\ 4 - x, & 3 < x \leq 4 \end{array} \right.$\\
then the number of points in the interval $( 0,4 )$ where $g ( x )$ is NOT differentiable, is $\underline{\hspace{1cm}}$.