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

• Correct answer
  A

  $(-\infty, \infty)$
• B

  $(-\infty, 0) \cup(0, \infty)$
• C

  $(0, \infty)$
• D

  $[0, \infty)$

Solution

Given that, $f(x)=x|x|$ $\therefore \quad f(x)=\left\{\begin{array}{cc}x^2 & , x \geq 0 \\ -x^2 & , x \lt 0\end{array}\right.$
It is clear from the graph that $f(x)$ is differentiable everywhere.

Hence, the correct answer is option: 'A'.