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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 35

  • question_answer
    If \[f(x)=2{{e}^{x}}-c{{\log }_{e}}x\]monotonically increases for every \[x\in (0,\infty ),\] then the true set of values of c is             

    A) \[\left( -\infty ,\frac{-1}{e} \right)\]           

    B)        \[\left( -\infty ,\frac{-2}{e} \right)\]           

    C) \[[0,\infty )\]                

    D)        \[(-\infty ,0]\]

    Correct Answer: D

    Solution :

    [d] \[f(x)=2{{e}^{x}}-c{{\log }_{e}}x\] \[f'(x)=2{{e}^{x}}-\frac{c}{x}\ge 0\] Now,         \[\frac{2x{{e}^{x}}-c}{x}\ge 0\forall x\in (0,\infty )\] \[\Rightarrow \,\,c\le 2x{{e}^{x}}\forall x\in (0,\infty )\] \[\Rightarrow \,\,c\le 0\]


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