Get Answers to all your Questions

header-bg qa

The function f(x)=\left(x^2-1\right)\left|x^2-3 x+2\right|+\cos (|x|) is not differentiable at

Option: 1

-1


Option: 2

0


Option: 3

1


Option: 4

2


Answers (1)

best_answer

\left(x^2-3 x+2\right)=(x-1)(x-2)=+ ive when \mathrm{x}<1 or >2, negative when 1 \leq \mathrm{x} \leq 2

Also \cos |\mathrm{x}|=\cos \mathrm{x}            \boxtimes \cos (-x)=\cos x
\therefore \quad f(x)=-\left(x^2-1\right)\left(x^2-3 x+2\right)+\cos x, 1 \leq x \leq 2 \\=\left(x^2-1\right)\left(x^2-3 x+2\right)+\cos x, x>2

Evidently f(x) is not differentiable at x=2 as L^{\prime} \neq R^{\prime}.

Note : For all other values like \mathrm{x}<0,0 \leq \mathrm{x}<1, \mathrm{f}(\mathrm{x}) is same as given by (A).

Posted by

seema garhwal

View full answer

JEE Main high-scoring chapters and topics

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