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

  • question_answer
    If from mean value theorem, \[f'({{x}_{1}})=\frac{f(b)-f(a)}{b-a}\], then                                                                       [MP PET 1999]

    A)            \[a<{{x}_{1}}\le b\]

    B)            \[a\le {{x}_{1}}<b\]

    C)            \[a<{{x}_{1}}<b\]

    D)            \[a\le {{x}_{1}}\le b\]

    Correct Answer: C

    Solution :

               According to mean value theorem,            In interval [a, b] for f (x)                     \[\frac{f(b)-f(a)}{b-a}=f'(c)\],  where \[a<c<b\]            \[\therefore a<{{x}_{1}}<b\].

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