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

  • question_answer
    \[2{{x}^{3}}+18{{x}^{2}}-96x+45=0\]is an increasing function when                                                               [RPET 1997]

    A)            \[x\le -8,\,x\ge 2\]

    B)            \[x<-2,x\ge 8\]

    C)            \[x\le -2,x\ge 8\]

    D)            \[0\le x\le -2\]

    Correct Answer: A

    Solution :

               \[f'(x)=6{{x}^{2}}+36x-96>0\], for increasing                    Þ \[f'(x)=(x+8)(x-2)\ge 0\]Þ\[x\ge 2,\ x\le -8\].


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