Let f : (0, 1) → be the function defined as f ( x ) = [4 x] (x- 1 4 )^ 2 (x- 1 2 ), where…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let f : (0, 1) → 
be the function defined as f(x) =\([4 x]\left(x-\frac{1}{4}\right)^{2}\left(x-\frac{1}{2}\right),\) where [x] denotes the greatest integer less than or equal to x . Then which of the following statements is(are) true?
be the function defined as f(x) =\([4 x]\left(x-\frac{1}{4}\right)^{2}\left(x-\frac{1}{2}\right),\) where [x] denotes the greatest integer less than or equal to x . Then which of the following statements is(are) true?- 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
Answer
(C) The function f is NOT differentiable at more than three points in (0,1)
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