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JEE Main & Advanced Sample Paper JEE Main Sample Paper-28

  • question_answer
    Let \[f(x)\] is differentiable function in \[[2,5]\] such that \[f(2)=\frac{1}{5}\] and \[f(5)=\frac{1}{2}\], then there exists a number \[c,2<c<5\] for which \[f(c)\] equals

    A)  \[\frac{1}{2}\]                                  

    B)  \[\frac{1}{5}\]

    C)  \[\frac{1}{10}\]                               

    D)  \[\frac{1}{15}\]

    Correct Answer: C

    Solution :

    Using, LMVT, \[f'(c)=\frac{f(5)-f(2)}{5-2}\Rightarrow f'(c)=\frac{\frac{1}{2}-\frac{1}{5}}{3}\] \[\Rightarrow f'(c)=\frac{1}{10}\]


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