Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  •  The set of points where the function    is differentiab

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

Option: 1

(-\infty, \infty)


Option: 2

(-\infty, 0) \cup(0, \infty)


Option: 3

(0, \infty)


Option: 4

[0, \infty]


Answers (1)

best_answer

We have \mathrm{f(x)=\left\{\begin{array}{l}x^2, x \geq 0 \\ -x^2, x<0\end{array}\right.} 
Clearly, f(x) is differentiable for all x>0 and for all x<0 So, we check the differentiability at x=0.
Now, \mathrm{(RHD~ at~ x=0)=\left(\frac{d}{d x}\left(x^2\right)\right)_{x=0}=(2 x)_{x=0}=0.}
and, \mathrm{( LHD~ at ~x=0)=\left(\frac{d}{d x}\left(-x^2\right)\right)_{x=0}=[-2 x]_{x=0}=0 }

\mathrm{\therefore \quad( LHD~ at ~x=0)=( RHD at ~x=0) }
So, f(x) is differentiable for all x i.e. the set of all points where f(x) is differentiable is \mathrm{(-\infty, \infty) } i.e. R.

Posted by

sudhir.kumar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

NTA Exams 2025 Live: NEET UG date, registration form soon at neet.nta.nic.in; UGC NET revised schedule out
anam-khan

Is it difficult to get into NIT Durgapur? JEE Main cut-offs for BTech programmes
anam-khan

JEE Main Deleted Syllabus 2025: Topics to skip this year; why no optional questions?

Latest Question