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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2006

  • question_answer
    Let\[f\]be a function such that\[f(1)=10\]and \[f(x)\ge 2\]for\[1\le x<4\]. How small can\[f(4)\]possibly be?

    A)  8              

    B)                         12

    C)  16                         

    D)         2

    E)  10

    Correct Answer: E

    Solution :

    Given \[f(x)\ge 2\] On integrating both sides w.r.t.\[x,\]we get \[f(x)\ge 2x+c\] \[\Rightarrow \] \[f(1)\ge 2\times 1+c\] \[\Rightarrow \] \[c\le 4-2\]\[\Rightarrow \] \[c\le 2\] \[\Rightarrow \] \[f(x)\ge 2x+2\] \[\therefore \]  \[f(4)\ge 2\times 4+2=10\]


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