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

  • question_answer
    The function \[y=2{{x}^{3}}-9{{x}^{2}}+12x-6\] is monotonic decreasing, when                                  [MP PET 1994]

    A)            \[1<x<2\]

    B)            \[x>2\]

    C)            \[x<1\]

    D)            None of these

    Correct Answer: A

    Solution :

               Here \[f(x)=y=2{{x}^{3}}-9{{x}^{2}}+12x-6\]                    \[\Rightarrow \]\[f'(x)=6{{x}^{2}}-18x+12\]                    Since\[f(x)\]is increasing or decreasing in \[(a,b)\] according as \[f'(x)>0\]or \[<0\]for every \[x\in (a,b)\].                    Hence \[f'(x)=6(x-2)(x-1)\] which is obviously decreasing if \[x\in (1,2)\,\,\,i.e.,\,1<x<2\].


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