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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2007

  • question_answer
        A function\[y=f(x)\]as a second order derivative\[f=6(x-1)\]. If its graph passes through the point (2, 1) and at that point the tangent to the graph is\[y=3x-5,\]then the function is

    A)  \[{{(x-1)}^{2}}\]                              

    B)  \[{{(x-1)}^{3}}\]

    C)  \[{{(x+1)}^{3}}\]                             

    D)  \[{{(x+1)}^{2}}\]

    Correct Answer: B

    Solution :

                    \[f\,(x)=6(x-1)\] \[\Rightarrow \]               \[f(x)=3{{(x-1)}^{2}}+c\]                   ...(i) At the point (2,1) the tangent to graph is \[y=3x-5.\] Slope of tangent \[=3\Rightarrow f(2)=3\] \[\therefore \]  \[f(2)=3{{(2-1)}^{2}}+c=3\] \[\Rightarrow \]               \[3+c=3\Rightarrow c=0\] \[\therefore \]From Eq. (i) \[f(x)=3{{(x-1)}^{2}}\] \[\Rightarrow \]               \[f(x)={{(x-1)}^{3}}+k\]       ....(ii) Since graph passes through (2,1) \[\therefore \]  \[1={{(2-1)}^{2}}+k\]                 \[k=0\] \[\therefore \]Equation of function is                 \[f(x)={{(x-1)}^{3}}\]


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