Question

The number of points, at which the function $f(x)=|2x+1|-3|x+2|+\left|x^2+x-2\right|,x\in R$ is not differentiable, is ____

Answer 1

Answer: 2

$f(x)=|2x+1|-3|x+2|+\left|x^2+x-2\right|$
$=|2x+1|-3|x+2|+|x+2||x-1|$
$=|2x+1|+|x+2|(|x-1|-3)$
Critical points are $x=\frac{-1}{2},-2,-1$
but $x=-2$ is making a zero. twice in product so, points of non
differentability are $x=\frac{-1}{2}$ and $x=-1$
$\therefore$ Number of points of non-differentiability $=2$