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

  • question_answer
    Function \[f(x)=2{{x}^{3}}-9{{x}^{2}}+12x+29\] is monotonically decreasing, when  [RPET 1996]

    A)            \[x<2\]

    B)            x > 2

    C)            x >1

    D)            1< x < 2

    Correct Answer: D

    Solution :

               Function is monotonically decreasing, when \[{f}'(x)<0\]                     Þ \[6{{x}^{2}}-18x+12<0\] Þ \[{{x}^{2}}-3x+2<0\]                    Þ  \[{{x}^{2}}-2x-x+2<0\] Þ \[(x-2)(x-1)<0\],                    \[\therefore x\in 1<x<2\].


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