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

(–∞, ∞) (–∞, 0) ∪ (0, ∞) (0, ∞) [0, ∞]

(–∞, ∞)

$f(x)=-x^2,x<0$ $=x^2,x≥0$ The function is differentiable for all x > 0 and for all x < 0. Take differentiability for x = 0. $∴L.H.D.=\underset{h→0}{\lim}\frac{-(-h)^2-0}{-h}=0$ $R.H.D.=\underset{h→0}{\lim}\frac{h^2-0}{h}=0$