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JEE Main & Advanced Mathematics Functions Question Bank Differentiability

  • question_answer
    If                                                                                     \[f(x)\,=\frac{x}{1+|x|}\]  for                                                                                                 \[x\in R,\]  then                                                                                                  \[f'(0)=\]                    [EAMCET 2003]

    A)            0

    B)            1

    C)            2

    D)            3

    Correct Answer: B

    Solution :

               Let                                                                                   \[x<0\Rightarrow |x|=-x\]  Þ                                                  \[f(x)=\frac{d}{dx}\left( \frac{x}{1-x} \right)=\frac{1}{{{(1-x)}^{2}}}\]                    Þ                                                                                      \[{{[{f}'(x)]}_{x=0}}=1\] . Again                                                                                                   \[x>0\]  Þ                                                                                               \[|x|\,=\,x\]                       \[f(x)=\frac{d}{dx}\left( \frac{x}{1+x} \right)=\frac{1}{{{(1+x)}^{2}}}\Rightarrow {{[{f}'(x)]}_{x=0}}=1\]            Þ                                                                                               \[{f}'(0)=1\] .


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