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

  • question_answer
    Which of the following is not a decreasing function on the interval \[\left( 0,\frac{\pi }{2} \right)\]

    A)            \[\cos x\]

    B)            \[\cos 2x\]

    C)            \[\cos 3x\]

    D)            \[\cot x\]

    Correct Answer: C

    Solution :

               Obviously here \[\cos 3x\]is not decreasing in \[\left( 0,\frac{\pi }{2} \right)\] because \[\frac{d}{dx}\cos 3x=-3\sin 3x\]                    But at \[x=75{}^\circ ,\,\,-3\sin 3x>0\]. Hence the result.


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