Let$\mathrm{f} \left(\mathrm{x}\right) = 1+ | \mathrm{x} - 2 | + | \sin \mathrm{x} |,$ then Lagrange’s mean value theorem is applicable for $\text{⨍ }\left(x\right)$ in

$|\mathrm{x}-2|$ not differentiable at x=2

$|\sin \mathrm{x}|$ not differentiable at $\mathrm{x}=0, \mathrm{\pi }, 2\mathrm{\pi }, 3\mathrm{\pi }$

$\therefore$ L.N.V.T applicable is $\left[\mathrm{\pi }, 2\mathrm{\pi }\right]$