Question:
The number of points, at which the function $\mathrm{f}(\mathrm{x})$ $=|2 x+1|-3|x+2|+\left|x^{2}+x-2\right|, x \in R$ is not differentiable, is______.
Solution:
$f(x)=|2 x+1|-3|x+2|+\left|x^{2}+x-2\right|$
$=|2 x+1|-3|x+2|+|x+2||x-1|$
$=|2 x+1|+|x+2|(|x-1|-3)$
Critical points are $\mathrm{x}=\frac{-1}{2},-2,-1$
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 $=2$