Mathematics - Continuity - Differentiability Question with Solution | TestHub

(A) $x|x|$ is continuous, differentiable and strictly increasing in $(-1,1)$. (B) $\sqrt{|x|}$ is continuous in $(-1,1)$ and not differentiable at $x=0$. (C) $x+[x]$ is strictly increasing in $(-1,1)$ and discontinuous at $x=0$ $\Rightarrow$ not differentiable at $x=0$. (D) $|x-1|+|x+1|=2$ in $(-1,1)$ The function is continuous and differentiable in $(-1,1)$.