Mathematics - Continuity - Differentiability Question with Solution | TestHub

Given,

$f\left(x\right)=\left[a+13 \sin x\right], x\in \left(0,\pi \right)$

$\Rightarrow f\left(x\right)=[13 \sin x]+a$, as $a\in \text{Integer}$

Now let $g\left(x\right)=13 \mathrm{sinx}$, now plotting the diagram of $y=13\sin x$ we get,

Now from above diagram we can see that,

$f\left(x\right)=\left[13 \mathrm{sinx}\right]$ is not differentiable at intersection points of $y=k, k\in [1,13] \& k\in Z$

$\Rightarrow$Points of non-differentiability$=12\times 2+1=25$