$\text{ If }f\left(x\right)=\left\{\begin{array}{ll}x{e}^{-\left(\frac{1}{\left|x\right|}+\frac{1}{x}\right)}& , x\ne 0\\ 0& , x=0\end{array}\text{ then }f\left(x\right)\right.\text{ is }$

continuous as well as differentiable for all $x$

Discontinuous every where

Neither differentiable nor continuous at $x$ =0

Continuous for all  but not differentiable at $x$=0