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

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

Let $f\left( x \right)=\left( x+\left| x \right| \right) \left| x \right|$. Then for all $x.$

If ;$\displaystyle f(x)=sgn(x^{5})$ then which of the following is/are false (where sgn denotes signum function)

The function $f\left( x \right)=\max { \left\{ \left( 1-x \right) ,\left( 1+x \right) ,2 \right\} } ,x\in \left( -\infty ,\infty \right)$ is