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JEE Advanced 2023 · Paper 2 · one or more correct

JEE Advanced 2023 Mathematics question on Limits Continuity and Differentiability

Let f:(0,1)→Rf:(0,1) \to \mathbb{R} be the function defined as f(x)=[4x](x−14)2(x−12)f(x) = [4x]\left(x - \dfrac{1}{4}\right)^2\left(x - \dfrac{1}{2}\right), where [x][x] denotes the greatest integer less than or equal to xx. Then which of the following statements is(are) true?
  1. A.
    The function ff is discontinuous exactly at one point in (0,1)(0,1)
  2. B.
    There is exactly one point in (0,1)(0,1) at which the function ff is continuous but NOT differentiable
  3. C.
    The function ff is NOT differentiable at more than three points in (0,1)(0,1)
  4. D.
    The minimum value of the function ff is −1512-\dfrac{1}{512}
Show answer

Correct options: A, B

[JEE Advanced 2023 · Paper 2]

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