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

Answer: 0

$f(x)=x(x-1)\left|e^x-11\cdot \right|x-{3|}^3$
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 $x\in R$