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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    The value of\[x\]for which the polynomial\[2{{x}^{3}}-9{{x}^{2}}+12x+4\]is a decreasing function of\[x,\] is:

    A)  \[-1<x<1\]         

    B) \[0<x<2\]

    C)  \[x>3\]               

    D)        \[1<x<2\]

    E)  \[1<x<3\]

    Correct Answer: D

    Solution :

    \[\because \]     \[f(x)=2{{x}^{3}}-9{{x}^{2}}+12x+4\] On differentiating w.r.t.\[x,\]we get \[f(x)=6{{x}^{2}}-18x+12\] For function to be decreasing \[f(x)<0\] \[\Rightarrow \]\[6({{x}^{2}}-3x+2)<0\] \[\Rightarrow \] \[({{x}^{2}}-2x-x+2)<0\] \[\Rightarrow \] \[(x-2)(x-1)<0\] \[\Rightarrow \]               \[1<x<2\]


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