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

  • question_answer
    In which interval is the given function \[f(x)=2{{x}^{3}}-15{{x}^{2}}+36x+1\] is monotonically decreasing  [RPET 1995]

    A)            [2, 3]

    B)            (2, 3)

    C)            \[(-\infty ,\,2)\]

    D)            \[(3,\,\infty )\]

    Correct Answer: B

    Solution :

               \[y=f(x)=2{{x}^{3}}-15{{x}^{2}}+36x+1\]            \[\frac{dy}{dx}=f'(x)=6{{x}^{2}}-30x+36=6({{x}^{2}}-5x+6)\]            \[f'(x)=6(x-2)(x-3)\]            To be monotonic decreasing, \[f'(x)<0\]            \[\Rightarrow (x-2)(x-3)<0\Rightarrow x\in (2,3)\].


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