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, \[\frac{2x{{e}^{x}}-c}{x}\ge 0\forall x\in (0,\infty )\] \[\Rightarrow \,\,c\le 2x{{e}^{x}}\forall x\in (0,\infty )\] \[\Rightarrow \,\,c\le 0\]You need to login to perform this action.
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