JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Rolle's theorem Lagrange's mean value theorem

  • question_answer
    The abscissa of the points of the curve \[y={{x}^{3}}\]in the interval [?2, 2], where the slope of the tangents can be obtained by mean value theorem for the interval [?2, 2], are                    [MP PET 1993]

    A)            \[\pm \frac{2}{\sqrt{3}}\]

    B)            \[\pm \sqrt{3}\]

    C)            \[\pm \frac{\sqrt{3}}{2}\]

    D)            0

    Correct Answer: A

    Solution :

               Given that equation of curve \[y={{x}^{3}}=f(x)\]            So \[f(2)=8\] and \[f(-2)=-8\]            Now \[f'(x)=3{{x}^{2}}\Rightarrow f'(x)=\frac{f(2)-f(-2)}{2-(-2)}\]            Þ\[\frac{8-(-8)}{4}=3{{x}^{2}};\,\,\,\,\therefore x=\pm \frac{2}{\sqrt{3}}\].

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