Question

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

Answer 1

$f(x) =|2 x+1|-3|x+2|+\left|x^{2}+x-2\right| $
$=|2 x+1|-3|x+2|+|x+2||x-1| $
$=|2 x+1|+|x+2|(|x-1|-3)$
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 $=2$