Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Fill in the blanks question 2

Provide solution for RD Sharma maths class 12 chapter 9 Differentiability exercise Fill in the blanks question  2

Answers (1)

Answer: x=\pm 1

Hint: If f is differentiable at all x\in R, we must showf'(x) exists at all x\in R

Given: g(x)=|x-1|+|x+1|

Solution:  we know that

\begin{aligned} g(x) &=\left\{\begin{array}{l} -x-1+1-x, x<-1 \\ x+1+1-x,-1 \leq x<1 \\ x-1+x+1, x \geq 1 \end{array}\right\} \\ &=\left\{\begin{array}{l} -2 x, x<-1 \\ 2,-1 \leq x<1 \\ 2 x, x \geq 1 \end{array}\right\} \end{aligned}

\begin{aligned} &g^{\prime}(x)=\left\{\begin{array}{l} -2, x<-1 \\ 0,-1 \leq x<1 \\ 2, x \geq 1 \end{array}\right\} \\\\ &g^{\prime}\left(-1^{-}\right)=-2, g^{\prime}\left(-1^{+}\right)=0 \end{aligned}

g^{\prime}\left(1^{-}\right)=0, g^{\prime}\left(1^{+}\right)=2

The above derivative calculations can be done from the first principle also.

Since LHS and RHS derivatives are not equal at the points 1 and -1.

 Hence the function is not differentiable at x=\pm 1.

 

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question