Let [.] denotes the greatest integer function,  $f:(0,1)-\left\{\frac{1}{3}\right\}\to R$ be the function defined as  $f\left(x\right)=\left[4x\right]{(x-\frac{1-\left[x\right]}{3})}^{\left[2x\right]}{(x-\frac{\left[2x\right]+1}{4})}^{{ }^{3+\left[x\right]}}$. Then which of the following options is/are correct?

The minimum value of f is 0

There exists exactly two points in $\left(0,1\right)$ at which the function f is continuous but NOT differentiable

The function f is discontinuous at exactly two points in its domain

The function f is NOT differentiable at more than three points in $(0,1)$