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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    Suppose that \[f(0)=-3\] and \[f'(x)=\,\le 5\] for all values of x. Then, the largest value which f(2) can attain is????               

    A) 7

    B) 10

    C) 2

    D) 9

    Correct Answer: A

    Solution :

    [a] Using LMVT in [0, 2] \[\frac{f(2)-f(0)}{2-0}=f'(c)\], where \[c\in (0,2)\] \[\frac{f(2)+3}{2}\le 5\Rightarrow f(2)\le 7\].


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