The number of point(s) of non-differentiability of $f (x) = [x] + | sin x |$ in $(0, 10)$ is
(where [.] denotes greatest integer function )

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Solution

Given : $f (x) = [x] + | sin x | and x \in (0, 10)$
We know, $[x]$ is not differentiable when $x \in Z$
$\Rightarrow$ It is not differentiable at $9$ integral points.
and $| sin x |$ is not differentiable when $x \in n π$ , where $n$ is an integer.
$\Rightarrow | sin x |$ is not differentiable at $x = π, 2 π, 3 π$
Hence, $f (x)$ is not differentiable at $12$ points.

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The number of point(s) of non-differentiability of f(x)=[x]+|sinx| in (0,10) is (where [.] denotes greatest integer function )

The number of point(s) of non-differentiability of $f (x) = [x] + | sin x |$ in $(0, 10)$ is
(where [.] denotes greatest integer function )