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VIT Engineering VIT Engineering Solved Paper-2009

  • question_answer
    If \[f:[2,\,3]\to R\] is defined by \[f(x)={{x}^{3}}+3x-2,\] then the range \[f(x)\] is contained in the interval

    A)  [1, 12]           

    B)  [12, 34]

    C)  [35, 50]          

    D)  [-12, 12]

    Correct Answer: B

    Solution :

    Given, \[f(x)={{x}^{3}}+3x-2\] On differentiating w.r.t. x, we get \[f(x)=3{{x}^{2}}+3\] Put     \[f(x)=0\Rightarrow 3{{x}^{2}}+3=0\] \[\Rightarrow \] \[{{x}^{2}}=-1\] \[\therefore \] \[f(x)\]is either increasing or decreasing. At \[x=2,\,f(2)={{2}^{3}}+3(2)-2=12\] At \[x=3,f(3)={{3}^{3}}+3(3)-2=34\] \[\therefore \]\[f(x)\in [12,34]\].


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