Exhaustive set of points where f(x) = x|x| is differentiable, is

(−∞, ∞) ∼ {0} (−∞, ∞) ∼ {0} (−∞, ∞) ∼ [−1] (−∞, ∞)

(−∞, ∞)

$f(x)=\left\{\begin{array}{c}x^2, &x \geq 0 \\ -x^2, &x<0\end{array}\right.$ Graph of f(x) indicates that f(x) is differentiable for (–∞, ∞)