JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q18

MathematicsSingle correct+4 / -1Question 18 of 90

The number of points, where the function $f:\mathbf R\to\mathbf R$ , $f(x)=|x-1|\cos|x-2|\sin|x-1|+(x-3)|x^2-5x+4|$ , is NOT differentiable, is :

Answer and worked solution

Official answer: B

First term. $|x-1|\sin|x-1|$ behaves like $(x-1)^2$ and $\cos|x-2|=\cos(x-2)$ : smooth.

Second term $(x-3)|x-1||x-4|$ has corners at $x=1$ and $x=4$ , since $x-3\ne0$ there. Two points.

(B)

Topics:Differentiability

JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 18