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

  • question_answer
    Local maximum and local minimum values of the function \[(x-1){{(x+2)}^{2}}\]are

    A)            ? 4, 0

    B)            0, ? 4

    C)            4, 0

    D)            None of these

    Correct Answer: B

    Solution :

               \[f'(x)=2(x-1)(x+2)+{{(x+2)}^{2}}=3{{x}^{2}}+6x\]            \[f'(x)=0\] Þ\[x=0,\,-2\]            \[f(-2)=(-2-1){{(-2+2)}^{2}}=0\]      (Maximum value)            and \[f(0)=(0-1){{(0+2)}^{2}}=-4\] (Minimum value).


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