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  4. 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

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Q. The number of points of non-differentiability of the function $f\left(\right.x\left.\right)=max\left(\right.sinx,2x\left.\right)+\left[\right.max\left(\right.sinx,2x\left.\right)\left]\right.$ (where $\left[\cdot \right]$ denotes greatest integer function) in $\left(\right.0,2\pi \left.\right)$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$max\left(sin x , 2 x\right)=2x$
$\therefore y=2x+\left[\right.2x\left]\right.$ is non differentiable at $12$ points