Differentiabilty

Q. If $f\left(x\right)=\text{min}\left\{x^2,-x+1,sgn|-x|\right\}$ then $f\left(x\right)$ is
(where $\text{sgn}\left(x\right)$ denotes signum function of $x$)

1. continuous at $x=0$
2. discontinuous at one point
3. non-differentiable at $3$ points
4. differentiable at $x=\frac{1}{2}$

Q. Let $f\left(x\right)=\{\begin{array}{cc}{x}^3,& x<0\\ x^2,& x\ge 0\end{array}$ then

1. $f\left(x\right)$ is continuous at $x=0$
2. $f\left(x\right)$ is differentiable at $x=0$
3. $f^{\prime }\left(x\right)$ is continuous on $R$
4. $f^{\prime \prime }\left(x\right)$ exists for all $xϵR$

Q. If $f\left(x\right)=\text{min}\left\{x^2,-x+1,sgn|-x|\right\}$ then $f\left(x\right)$ is
(where $\text{sgn}\left(x\right)$ denotes signum function of $x$)

1. continuous at $x=0$
2. discontinuous at one point
3. non-differentiable at $3$ points
4. differentiable at $x=\frac{1}{2}$