JEE Advanced 2023 | Differentiability PYQ | Maths PYQ | Full Concepts Explain | LCD скачать в хорошем качестве

JEE Advanced 2023 | Differentiability PYQ | Maths PYQ | Full Concepts Explain | LCD

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? (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 JEE Advanced 2023 This is a very conceptual JEE Advanced 2023 PYQ from Functions (Differentiability + Continuity) involving Greatest Integer Function [x]. 📌 Full Question: Let f:(0,1)\to \mathbb{R} be the function f(x)=\left(x^2-\frac14\right)\left(x-\frac12\right)\,[4x], \quad x\in(0,1) where [x] is the greatest integer ≤ x. Choose the correct statement(s): (A) discontinuous exactly at one point (B) exactly one point continuous but not differentiable (C) not differentiable at more than three points (D) minimum value is -\frac{1}{512} In this lecture, we convert the function into a piecewise function using values of [4x] and then analyze: • continuity points • differentiability points • minimum value 📌 Subscribe for daily JEE Advanced PYQ solutions.