Functions Question 488
Question: The function $ f(x)=(x^{2}-1)|x^{2}-3x+2|+\cos (|x|) $ is not differentiable at
[IIT 1999]
Options:
A) -1
B) 0
C) 1
D) 2
Show Answer
Answer:
Correct Answer: D
Solution:
Since function $ |x| $ is not differentiable at $ x=0 $
$ \therefore ,|x^{2}-3x+2|=|(x-1)(x-2)| $ Hence is not differentiable at $ x=1 $ and 2 Now $ f(x)=(x^{2}-1)|x^{2}-3x+2|\cos (|x|) $ is not differentiable at $ x=2 $ For $ 1<x<2 $ , $ f(x)=-(x^{2}-1)(x^{2}-3x+2)+\cos x $ For $ 2<x<3 $ , $ f(x)=+(x^{2}-1)(x^{2}-3x+2)+\cos x $ $ Lf’(x)=-(x^{2}-1)(2x-3)-2x(x^{2}-3x+2)-\sin x $ $ Lf’(2)=-3-\sin 2 $ $ Rf’(x)=(x^{2}-1)(2x-3)+2x(x^{2}-3x+2)-\sin x $ $ Rf’(2)=(4-1)(4-3)+0-\sin 2=3-\sin 2 $ Hence $ Lf’(2)\ne Rf’(2) $ .
BETA
