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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    If \[f(x)\] is a differentiable function satisfying \[f(x)<2\] for all \[x\in R\] and \[f(1)=2,\] then greatest possible integral value of \[f(3)\] is -

    A) 5         

    B) 6    

    C) 7                                 

    D) 8

    Correct Answer: A

    Solution :

    [A] \[\frac{f\,(3)-f\,(1)}{3-1}=f'\,(c),\] for some c such that \[1<c<3\] \[f'\,(c)=\frac{f\,(3)-2}{2}<2\] \[\therefore f(3)<6\]                    


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