The function `f(x)=e^(-|x|)` is continuous everywhere but not differentiable at `x=0` continuous and differentiable everywhere not continuous at `x=0` none of these

Explanation

Given `f(x)={e^(−x),x>=0 and e^x,x<0}`

LHL=`lim_(x->0^(−))f(x)=lim_(x->0)e^x=1`

RHL=`lim_(x->0^(+))f(x)=lim_(x->0)e^(−x)=1`

Also, `f(0)=e^0=1`

so,`LHL=RHL=f(0)`

Therefore, It is continuous for every value of x.

Now LHL at x=0

`(d/dz)(e^x)_(x=0)=[e^x]_(x=0)=e^0=1`

...