Mathematics - Continuity - Differentiability Question with Solution | TestHub

Given,$f\left(x\right)=\left|x-1\right|\cos \left|x-2\right|\sin \left|x-1\right|+\left(x-3\right)\left|x^2-5x+4\right|$

$=\left|x-1\right|\cos \left|x-2\right|\sin \left|x-1\right|+\left(x-3\right)\left|x-1\right|\left|x-4\right|$

$=\left|x-1\right|\left[\cos \left|x-2\right|\sin \left|x-1\right|+\left(x-3\right)\left|x-4\right|\right]$

We know that modulus function is not differentiable at values where modulus function is zero

So, we can say that function is non-differentiable at $x=1$ and $x=4$.