Let $$f: R \to R$$ be a function defined by $$f(x) = \text{Min}\{x + 1, |x| + 1\}$$. Then which of the following is true?

A

$$f(x) \ge 1$$ for all $$x \in R$$

B

$$f(x)$$ is not differentiable at $$x = 1$$

C

$$f(x)$$ is differentiable everywhere

D

$$f(x)$$ is not differentiable at $$x = 0$$