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

  • question_answer
    For the function\[x+\frac{1}{x},x\in [1,\,3]\], the value of c for the mean value theorem is                                          [MP PET 1997]

    A)            1

    B)            \[\sqrt{3}\]

    C)            2

    D)            None of these

    Correct Answer: B

    Solution :

               \[f'(x)=1-\frac{1}{{{x}^{2}}}\Rightarrow f'(c)=1-\frac{1}{{{c}^{2}}}\]            \[\therefore 1-\frac{1}{{{c}^{2}}}=\frac{\frac{10}{3}-2}{2}\Rightarrow 1-\frac{1}{{{c}^{2}}}=\frac{2}{3}\Rightarrow {{c}^{2}}=3\].

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