Let $f:R\rightarrow R$ be a function defined by $f\left(x\right)=Min \left\{x+1, \left|x\right|+1\right\}$. Then which of the following is true?

The function $f(x)=|x|+|x-1|$ is

Which of the following function is thrice differentiable at x=0?

If $f(x)$ = $x^{3}$ sgn x, then

If $f '$ (0) = 0 and f(x) is a differentiable and increasing function,then lim $x \rightarrow 0$  $\frac {x.f ' (x^2)}{f ' (x)}$