The number of points of non-differentiability of the function f(.x.)=max(.sinx,2x.)+[.max(.sinx,2x.)]. (where [⋅ ] denotes greatest integer function) in (.0,2π .) is

Question

The number of points of non-differentiability of the function f(.x.)=max(.sinx,2x.)+[.max(.sinx,2x.)]. (where [⋅ ] denotes greatest integer function) in (.0,2π .) is (A) 12 (B) 14 (C) 17 (D) 18

Tardigrade Admin · Accepted Answer

max(sin x , 2 x)=2x ∴ y=2x+[.2x]. is non differentiable at 12 points

Q. The number of points of non-differentiability of the function $f (x) = ma x (s in x, 2 x) + [ma x (s in x, 2 x)]$ (where $[\cdot]$ denotes greatest integer function) in $(0, 2 π)$ is

$12$

$14$

$17$

$18$

$ma x (s in x, 2 x) = 2 x$
$∴ y = 2 x + [2 x]$ is non differentiable at $12$ points

Q. The number of points of non-differentiability of the function f(x)=max(sinx,2x)+[max(sinx,2x)] (where [⋅] denotes greatest integer function) in (0,2π) is

12

14

17

18