A) (0, e)
B) (0, 1)
C) (0, 1/e)
D) None of these
Correct Answer: C
Solution :
Let \[f(x)={{x}^{x}}\] \[f(x)={{x}^{x}}[1+\log x]={{x}^{x}}(\log e+\log x)\] \[={{x}^{x}}(\log ex)\] Put \[f(x)=0\Rightarrow {{x}^{x}}(\log ex)=0\] \[\Rightarrow \] \[x=0,1/e\] Hence, function decreases in the interval \[(0,1/e).\]You need to login to perform this action.
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