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

  • question_answer
    For the function\[f(x)={{e}^{x}},a=0,b=1\], the value of c in mean value theorem will be                                               [DCE 2002]

    A)            log x

    B)            \[\log (e-1)\]

    C)            0

    D)            1

    Correct Answer: B

    Solution :

               Here \[\frac{f(b)-f(a)}{b-a}=f'(c)\]                    Þ \[\frac{{{e}^{b}}-{{e}^{a}}}{b-a}=f'(c)\]Þ\[\frac{e-1}{1-0}={{e}^{c}}\Rightarrow c=\log (e-1)\].

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