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

  • question_answer
    The function \[\sin x-\cos x\]is increasing in the interval

    A)            \[\left[ \frac{3\pi }{4},\frac{7\pi }{4} \right]\]

    B)            \[\left[ 0,\frac{3\pi }{4} \right)\]

    C)            \[\left[ \frac{\pi }{4},\frac{3\pi }{4} \right]\]

    D)            None of these

    Correct Answer: B

    Solution :

               We have, \[f'(x)=\cos x+\sin x\]               Now \[f(x)\]is increasing function of x, if            \[f'(x)=\cos x+\sin x>0\]or \[\sqrt{2}\cos \left( x-\frac{\pi }{4} \right)>0\]            Þ\[0\le x<\frac{3\pi }{4}i.e.\,\,\,f'(x)>0\]in \[\left[ 0,\frac{3\pi }{4} \right)\].


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