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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    The number of continuous and derivable function(s) \[f(x)\] such that \[f(1)=-1,\,\,f(4)=7\] and \[f'(x)>3\] for all \[x\in R\] is/are

    A)  0                                            

    B)  1

    C)  2                                            

    D)  infinite

    Correct Answer: A

    Solution :

    Using LMVT in [1,4] for \[y=f(x)\] there must exist at least one \[c\in (1,4)\]such that \[f'(c)=\frac{f(4)-f(1)}{4-1}=\frac{8}{3}\]but \[f'(x)>3\forall x\in R\] Hence, no such function exists.


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