Applications Of Derivatives Question 331
Question: The function $ f(x)=x+\sin x $ has
[AMU 2000]
Options:
A) A minimum but no maximum
B) A maximum but no minimum
C) Neither maximum nor minimum
D) Both maximum and minimum
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=x+\sin x $
therefore $ {f}’(x)=1+\cos x $
Now $ {f}’(x)=0\Rightarrow 1+\cos x=0\Rightarrow \cos x=-1\Rightarrow x=\pi $
Now $ {f}’’(x)=-\sin x $ , $ {f}’’(\pi )=0 $ , $ f’’’(x)=-\cos x $ ,
$ {f}’’’(\pi )=1\ne 0 $ Neither maximum nor minimum.
BETA
