The number of points, at which the function f(x) = max \ 6x, 2 + 3x 2\ + x - 1 cos x 2 - 1/4 , xin (-π ,π) , is not differentiable, is .

Mathematics · Limits, Continuity and Differentiability

JEE Main 2026 — 4 April, Morning Shift — Question 47

The number of points, at which the function $\mathrm{f(x)} = \max \{6x, 2 + 3x^2\} +|x - 1| \cos \left|x^2 - \frac{1}{4}\right|, x\in (-\pi ,\pi)$ , is not differentiable, is ______.

Answer: 3

Numerical answer — enter this value.

Step-by-step solution

$2+3 \mathrm{x}^{2}=6 \mathrm{x} \Rightarrow 3 \mathrm{x}^{2}-6 \mathrm{x}+2=0$ $\mathrm{x}=\frac{6 \pm \sqrt{12}}{6}=\frac{3 \pm \sqrt{2}}{3}$ $|\mathrm{x}-1| \cos \left|\mathrm{x}^{2}-\frac{1}{4}\right|$ is not differentiable at $\mathrm{x}=1$ Total number of points where $f(x)$ is non Differentiable is $3$

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Exam: JEE Main 2026
Paper: 4 April, Morning Shift
Subject: Mathematics
Chapter: Limits, Continuity and Differentiability
Topic: Differentiability