The number of points, at which the function $f\left ( x \right )=\left | 2x+1 \right |-3\left | x+2 \right |+\left | x^{2}+x-2 \right |,x\in R$ is not differentiable, is _______ Option: 1 0 Option: 2 1 Option: 3 2 Option: 4 4

\begin{aligned}\mathrm{f}(\mathrm{x})&space;&=|2&space;\mathrm{x}+1|-3|\mathrm{x}+2|+\left|\mathrm{x}^{2}+\mathrm{x}-2\right|&space;\\&=|2&space;\mathrm{x}+1|-3|\mathrm{x}+2|+|\mathrm{x}+2||\mathrm{x}-1|&space;\\&=|2&space;\mathrm{x}+1|+|\mathrm{x}+2|(|\mathrm{x}-1|-3)\end{aligned}

$\text&space;{&space;Critical&space;points&space;are&space;}&space;x=\frac{-1}{2},-2,-1$

but x = -2 is making a zero. twice in product

So, points of non differentability are $x=\frac{-1}{2}$ and x = -1

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