The function $f(x)=e^{|x|}$ is

Question

$$\begin{array}{1 1}(A)\;continuous \;everywhere \;but\;not\;differentiable\;at\;x=0\\(B)\;continuous\;and\;differentiable\;every where\\(C)\;not\;continuous\;at\;x=0\\(D)\;none\;of\;these.\end{array}$$