Let f:(0,1) \to \mathbb{R} be the function defined as f(x)=[4 x] (x-\frac{1}{4}) ^2 (x-\frac{1}{2}), where [x] denotes the greatest integer less than or equal to x. Then which of the following is(are) true? [JEE Adv 2023 P2]

The function f is discontinuous exactly at one point in (0,1)

There is exactly one point in (0,1) at which the function f is continuous but NOT differentiable

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

The minimum value of the function f is -\frac{1}{512}

Limits, Continuity and Differentiability

Section: Mathematics

Question : 9 of 51

Marks: +1, -0

Let f:(0,1)→ℝ be the function defined as f(x)=[4x](x−‌

)2(x−‌

), where [x] denotes the greatest integer less than or equal to x. Then which of the following is(are) true?

[JEE Adv 2023 P2]

The function f is discontinuous exactly at one point in (0,1)
There is exactly one point in (0,1) at which the function f is continuous but NOT differentiable
The function f is NOT differentiable at more than three points in (0,1)
The minimum value of the function f is −‌
1
512

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