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J & K CET Engineering J and K - CET Engineering Solved Paper-2008

  • question_answer
    The   function \[f(x)=2{{x}^{3}}+3{{x}^{2}}-12x+1\] decreases in the interval                    

    A)  \[(2,3)\]          

    B)  \[(1,2)\]

    C)  \[(-2,1)\]        

    D)  \[(-3,-2)\]

    Correct Answer: C

    Solution :

    Given,  \[f(x)=2{{x}^{3}}+3{{x}^{2}}-12x+1\] \[\Rightarrow \] \[f'(x)=6{{x}^{2}}+6x-12\] For \[f(x)\] to be decreasing, \[f'(x)<0\] \[\Rightarrow \] \[6{{x}^{2}}+6x-12<0\] \[\Rightarrow \] \[{{x}^{2}}+x-2<0\] \[\Rightarrow \] \[(x+2)(x-1)<0\] \[\Rightarrow \] \[x\in (-2,1)\]


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