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  • The set of points where the function is differentiable is  

The set of points where the function \mathrm{f(x)=x|x|} is differentiable is
 

Option: 1

\mathrm{(-\infty, \infty)}
 


Option: 2

\mathrm{(-\infty, 0) \cup(0, \infty)}
 


Option: 3

\mathrm{(0, \infty)}

 


Option: 4

\mathrm{[0, \infty]}


Answers (1)

best_answer

\mathrm{f(x) =-x^2, \quad x<0 }

\mathrm{=x^2, \quad x \geq 0 }

The function is differentiable for all \mathrm{x>0} and for all \mathrm{x<0}.

Take differentiability for \mathrm{ x=0.}

\mathrm{ \therefore \text { L.H.D. }=\lim _{h \rightarrow 0} \frac{-(-h)^2-0}{-h}=0 }

\mathrm{ \text { R.H.D. }=\lim _{h \rightarrow 0} \frac{h^2-0}{h}=0}

Hence option 1 is correct.



 

Posted by

Pankaj Sanodiya

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