The set of points where the function f (x) = x | x | is differentiable is
Answer & explanation
Correct answer: option 1
$f(x)=-x^2,x<0$
$=x^2,x≥0$
The function is differentiable for all x > 0 and for all x < 0.
Take differentiability for x = 0.
$∴L.H.D.=\underset{h→0}{\lim}\frac{-(-h)^2-0}{-h}=0$
$R.H.D.=\underset{h→0}{\lim}\frac{h^2-0}{h}=0$