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

  • question_answer
    The function \[f(x)={{x}^{3}}-6{{x}^{2}}+ax+b\] satisfy the conditions of Rolle's theorem in [1, 3]. The values of a and b are

    A)            11, ? 6

    B)            ? 6, 11

    C)            ?11, 6

    D)            6, ?11

    Correct Answer: A

    Solution :

               \[f(1)=f(3)\Rightarrow a+b-5=3a+b-27\Rightarrow a=11\], which is given in option  only.


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