Let $f : ( 0,1 ) \rightarrow \mathbb { R }$ be the function defined as $f ( x ) = [ 4 x ] \left( x - \frac { 1 } { 4 } \right) ^ { 2 } \left( x - \frac { 1 } { 2 } \right)$, where $[ x ]$ denotes the greatest integer less than or equal to $x$. Then which of the following statements is(are) true?
(A) The function $f$ is discontinuous exactly at one point in $( 0,1 )$
(B) There is exactly one point in $( 0,1 )$ at which the function $f$ is continuous but NOT differentiable
(C) The function $f$ is NOT differentiable at more than three points in $( 0,1 )$
(D) The minimum value of the function $f$ is $- \frac { 1 } { 512 }$