Let f: (0, 1) R 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?

JEE Advanced 2023 Mathematics question

Let be the function defined as , where denotes the greatest integer less than or equal to . Then which of the following statements is(are) true?

(A)The function is discontinuous exactly at one point in Correct
(B)There is exactly one point in at which the function is continuous but **NOT** differentiableCorrect
(C)The function is **NOT** differentiable at more than three points in
(D)The minimum value of the function is

Answer: (A),(B)

jumps at . At and the factors and vanish, so is continuous; at : but – discontinuous. (A) true. At

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Question ID VK-034118