Question

Number of points of non-differentiability of the function $f(x)=x(x-1)\left|e^{x}-1\right| \cdot|x-3|^{3}$ on $x \in(-\infty, \infty)$ is equal to ______.

Answer 1

$f(x)=x(x-1)\left|e^{x}-11 \cdot\right| x-\left.3\right|^{3}$
Here, $x=0$ and 3 are repeated roots of $f(x)=0$
So, there is no point where $f(x)$ is non-differentiable for all $x \in R$