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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer
        If\[f(x)\]is an even differentiable function on R, then\[f(x)\]is

    A)  an even function

    B)  an odd function

    C)  cant say

    D)  cant be determined

    Correct Answer: B

    Solution :

                    Since,\[f(x)\]is an even function \[\therefore \]  \[f(-x)=f(x),\forall \,x\in R\] On differentiating both sides w.r.t.\[x,\]we get                 \[-f-(x)=f(x)\,\,\forall \,x\in R\] \[\Rightarrow \]               \[f-(x)=-f(x)\,\,\forall \,x\in R\] Which shows that\[f(x)\]is an odd function.


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