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

  • question_answer
    The function \[f(x)=\cos x-2px\] is monotonically decreasing for                 [RPET  1987; MP PET 2002]

    A)            \[p<\frac{1}{2}\]

    B)            \[p>\frac{1}{2}\]

    C)            \[p<2\]

    D)            \[p>2\]

    Correct Answer: B

    Solution :

               \[f(x)\]will be monotonically decreasing, if\[f'(x)<0\].            Þ  \[f'(x)=-\sin x-2p<0\]Þ\[\frac{1}{2}\sin x+p>0\]            Þ  \[p>\frac{1}{2}\,,\,\,[\because -1\le \sin x\le 1]\].


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