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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Maxima and Minima

  • question_answer
    The function \[f(x)=x+\sin x\] has  [AMU 2000]

    A)            A minimum but no maximum

    B)            A maximum but no minimum

    C)            Neither maximum nor minimum

    D)            Both maximum and minimum

    Correct Answer: C

    Solution :

               \[f(x)=x+\sin x\] Þ \[{f}'(x)=1+\cos x\]            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.


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