Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

The function f(x) = (x2 – 1) |x2 – 3x + 2| + cos (|x|) is not differentiable at

Option: 1

x = –1


Option: 2

x = 0


Option: 3

x = 1


Option: 4

x = 2


Answers (1)

best_answer

Since cos (–x) = cos x

 cos | x | is differentiable for each 

\text { Also, } x^2-3 x+2>0 \Rightarrow(x-2)(x-1)>0

$$ \Rightarrow \quad x \in(-\infty, 1) \cup(2, \infty) $$ Similarly, $$ x^2-3 x+2<0 \Rightarrow x \in(1,2)If g(x)=\left(x^2-1\right)\left|x^2-3 x+2\right|then f (x) is not differentiable at points where g(x) is so.

Now,g(x)=(x-1)^2(x+1)(x-2), \forall x \in(-\infty, 1) \cup(2, \infty)

and =-(x-1)^2(x+1)(x-2) \forall x \in(1,2)

g (x) is not differentiable at x = 2

f (x) is not differentiable at x = 2.

Hence (D) is correct answer.

 

Posted by

jitender.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

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question