The set of all points where the function f(x) = x is differentiable is

\(f(x)=\left\{\begin{matrix}x^2&,& x≥0 \\ -x^2&, & x < 0\end{matrix}\right.\)

$LHL(0)=RHL(0)=0$

$f'(x)=\left\{\begin{matrix}2x&,& x≥0 \\ -2x&, & x < 0\end{matrix}\right.$

$LHD(0)=RHD(0)=0$

continuous and differentiable for $x∈(– ∞, ∞)$