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JEE Main & Advanced Mathematics Functions Question Bank Differentiability

  • question_answer
    Let f be continuous on [1, 5] and differentiable in (1, 5). If \[f(1)\]=?3 and \[f'(x)\ge 9\] for all \[x\in (1,\ 5)\], then [Kerala (Engg.) 2005]

    A)            \[f(5)\ge 33\]

    B)            \[f(5)\ge 36\]

    C)            \[f(5)\le 36\]

    D)            \[f(5)\ge 9\]

    E)            \[f(5)\le 9\]

    Correct Answer: B

    Solution :

               \[f(1)=-3\];  \[f'(x)\ge 9\] for all \[x\in (1,5)\];  \\[f(5)\ge 36\].


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