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

  • question_answer
    The interval of the decreasing function \[f(x)={{x}^{3}}-{{x}^{2}}-x-4\]is

    A)            \[\left( \frac{1}{3},\,1 \right)\]

    B)  \[\left( -\frac{1}{3},1 \right)\]

    C)            \[\left( -\frac{1}{3},\,\frac{1}{3} \right)\]

    D)   \[\left( -1,-\frac{1}{3} \right)\]

    Correct Answer: B

    Solution :

               Given \[f(x)={{x}^{3}}-{{x}^{2}}-x-4\]            This function will be decreasing function when \[f'(x)<0\]            Þ \[3{{x}^{2}}-2x-1<0\Rightarrow 3{{x}^{2}}-3x+x-1<0\]            Þ \[(3x+1)(x-1)<0\]; \[\therefore 3x+1>0\]and \[x-1<0\]            \[x>-\frac{1}{3}\]and \[x<1\] :\[\therefore x\in \left( \frac{-1}{3},\,1 \right)\] .


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