The function $f(x)=|x-3|, x \in R$ is:

differentiable for all $x \in R$ differentiable only at x = 3 no where continuous differentiable for all $x \in R$, except x = 3

differentiable for all $x \in R$, except x = 3

The correct answer is Option (4) → differentiable for all $x \in R$, except x = 3