Question

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

• A. Continuous as well as differentiable for all x
• B. Continuous for all x but not differentiable at x = 0
• C. Neither continuous at x = 0 nor differentiable
• D. f is differentiable at x = 0 but not at x = 1

Answer 1

The correct option is B Continuous for all x but not differentiable at x = 0

$f\left(x\right)=\begin{array}{cc}x{e}^{\circ }& ifx<0\\ x{e}^{\frac{-2}{x}}& ifx>0\\ 0& ifx=0\end{array}$