Question

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

• A. $f\left(x\right)$ is differentiable everywhere
• B. $f\left(x\right)$ is differentiable at $x=0$
• C. $f\left(x\right)\ge 1$ for all $xϵR$
• D. $f\left(x\right)$ is not differentiable at $x=1$

Answer 1

Answer: (A), (B)

The correct options are
A $f\left(x\right)$ is differentiable everywhere
B $f\left(x\right)$ is differentiable at $x=0$