2. Solved Papers
  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • 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:

    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: A

    Solution :

    By Lagrange mean value theorem \[f(x)=\frac{f(5)-f(1)}{5-1}\ge 9\] \[\Rightarrow \]               \[\frac{f(5)+3}{4}\ge 9\] \[\Rightarrow \]               \[f(5)\ge 36-3\] \[\Rightarrow \]               \[f(5)\ge 33\]


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