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  4. The number of points, where the function f: R arrow R , f ( x )=| x -1| cos | x -2| sin | x -1| +(x-3)|x2-5 x+4|, is NOT differentiable, is:

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Q. The number of points, where the function $f : R \rightarrow R , f ( x )=| x -1| \cos | x -2| \sin | x -1|$ $+(x-3)\left|x^2-5 x+4\right|$, is NOT differentiable, is:

JEE MainJEE Main 2022Continuity and Differentiability

Solution:

$f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3)\left|x^2-5 x+4\right|$
$ =|x-1| \cos |x-2| \sin |x-1|+(x-3)|x-1||x-4|$
$ =|x-1|[\cos |x-2| \sin |x-1|+(x-3)|x-4|]$
Non differentiable at $x=1$ and $x=4$.