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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Maxima and Minima

  • question_answer
    The function \[f(x)=2{{x}^{3}}-3{{x}^{2}}-12x+4\] has [DCE 2002]

    A)            No maxima and minima

    B)            One maximum and one minimum

    C)            Two maxima

    D)            Two minima

    Correct Answer: B

    Solution :

               \[f(x)=2{{x}^{3}}-3{{x}^{2}}-12x+4\]            \[{f}'(x)=6{{x}^{2}}-6x-12\]            Now \[{f}'(x)=0\] Þ \[{{x}^{2}}-x-2=0\] Þ \[x=2,\,-1\]            Now \[{f}''(x)=12x-6\] Þ \[{f}''(2)=+ve\], \[{f}''(-1)=-ve\]                    \Given function has one maximum and one minimum.


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