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

  • question_answer
    If x tends 0 to \[\pi \], then the given function \[f(x)=x\sin x+\cos x+{{\cos }^{2}}x\] is

    A)            Increasing                             

    B)            Decreasing

    C)            Neither increasing nor decreasing

    D)            None of these

    Correct Answer: B

    Solution :

               \[f(x)=x\sin x+\cos x+{{\cos }^{2}}x\]                    \[\therefore f'(x)=\sin x+x\cos x-\sin x-2\cos x\sin x\]                              \[=\cos x(x-2\sin x)\]                    Hence \[x\to 0\] to \[\pi \], then \[f'(x)<0\]                    i.e., \[f(x)\]is decreasing function.


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