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

  • question_answer
    For which interval, the function \[\frac{{{x}^{2}}-3x}{x-1}\] satisfies all the conditions of Rolle's theorem               [MP PET 1993]

    A)            [0, 3]

    B)            [? 3, 0]

    C)            [1.5, 3]

    D)            For no interval

    Correct Answer: D

    Solution :

               Here \[f(x)=\frac{{{x}^{2}}-3x}{x-1}\] Þ\[-\sin c=-\frac{2}{\pi }\Rightarrow c={{\sin }^{-1}}\left( \frac{2}{\pi } \right)\]            Obviously, it is not derivable at \[x=1\] i.e., in \[(0,3)\]            Also \[f(a)=f(b)\]does not hold for \[[-3,\,0]\] and  [1. 5, 3]            Hence the answer is .

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