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

  • question_answer
    Let \[f(x)=\sqrt{x-1}+\sqrt{x+24-10\sqrt{x-1};}\] \[1<x<26\] be real valued function. Then \[f\,'(x)\] for \[1<x<26\] is           [MP PET 2000]

    A)            0

    B)            \[\frac{1}{\sqrt{x-1}}\]

    C)            \[2\sqrt{x-1}-5\]

    D)            None of these

    Correct Answer: A

    Solution :

               From Rolle?s theorem in (1, 26), \[f(1)=f(26)=5\]. In given interval, function satisfy all the conditions of Rolle's theorem, therefore in [1, 26], at least, there is a point for which \[{f}'(x)=0\].

You need to login to perform this action.
You will be redirected in 3 sec spinner