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Let f:(0,1) to RR be the function define...

Let `f:(0,1) to RR` be the function defined as `f(x)=[4x](x-1/4)^2(x-1/2)`, 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 `-1/512`

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