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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Increasing and Decreasing Function

  • question_answer
    If \[f(x)=\sin x-\cos x,\] the function decreasing in \[0\le x\le 2\pi \] is                                                    [UPSEAT 2001]

    A)            \[[5\pi /6,\,3\pi /4]\]

    B)            \[[\pi /4,\,\pi /2]\]

    C)            \[[3\pi /2,\,5\pi /2]\]

    D)            None of these

    Correct Answer: D

    Solution :

               \[f(x)=\sin x-\cos x\]            \[{f}'(x)=\cos x+\sin x=\sqrt{2}\left[ \cos \,\,\left( x-\frac{\pi }{4} \right) \right]\]=\[\sqrt{2}\cos \left( x-\frac{\pi }{4} \right)\]            For \[f(x)\] decreasing, \[{f}'(x)<0\]            \[\frac{\pi }{2}<\left( x-\frac{\pi }{4} \right)<\frac{3\pi }{2}\],   (within \[0\le x\le 2\pi \]).            Þ  \[\frac{3\pi }{4}<x\le \frac{7\pi }{4}\].


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