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

  • question_answer
    If \[f(x)=2{{x}^{3}}-3{{x}^{2}}-12x+5\]and \[x\in [-2,\,4]\], then the maximum value of function is at the following value of x                          [MP PET 1987, 2000; Orissa JEE 2005]

    A)            2

    B)            ?1

    C)            ? 2

    D)            4

    Correct Answer: D

    Solution :

               \[f'(x)=6{{x}^{2}}-6x-12\]                    \[f'(x)=0\Rightarrow (x-2)(x+1)=0\Rightarrow x=-1,\,2\]                    Here \[f(4)=128-48-48+5=37\]                    \[f(-1)=-2-3+12+5=12\]                    \[f(2)=16-12-24+5=-15\]                    \[f(-2)=-16-12+24+5=1\]                    Therefore the maximum value of function is 37 at \[x=4\].


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