question_answer

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

A) \[(-\infty ,\,\,\infty )\]                  

B) \[(-\infty ,\,\,0)\cup (0,\,\,\infty )\]

C) \[(0,\,\,\infty )\]              

D)        \[[0,\,\,\infty )\]

Correct Answer: A

Solution :

Given that,         \[f(x)=x|x|\] \[\therefore \]  \[f(x)=\left\{ \begin{matrix}    {{x}^{2}}, & x\ge 0  \\    -{{x}^{2}}, & x<0  \\ \end{matrix} \right.\] It is clear from the graph that\[f(x)\]is differentiable everywhere.