The function f(x)=x2−1x2−3x+2+cos |x| is not differentiable at

$f (x) = (x + 1) (x - 1) | x - 1 | x - 2 ∣ + \cos x$ .

because

$\cos | x | = \{\begin{array}{ll} \cos x, if x \geq 0 \\ \cos (- x), if x < 0 \end{array} = \cos x$ .

Since $h (x) = x | x |$ is differentiable at $x = 0$ , So $(x - 1) | x - 1 |$

is differentiable at $x = 1$ Also $f (x)$ is not differentiable at $x = 2$ .

The function $f (x) = (x^{2} - 1) |x^{2} - 3 x + 2| + \cos | x |$ is not differentiable at