Let \( f:(0,1)\to \mathbb{R} \) be the function defined as \( f(x)=[4x]\left(x-\frac{1}{4}\right)^{2}\left(x-\frac{1}{2}\right) \), where \( [x] \) denotes the greatest integer less than or equal to \( x \). Then which of the following statements is(are) true?
