The function $$f(x)={{x}^{1/x}}$$ is [AMU 2002]

Question

The function                                                                                      $$f(x)={{x}^{1/x}}$$ is                                                          [AMU 2002]

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Decreasing in                                                                                              $$(1,\,e),$$  increasing in                                                                                            $$(e,\infty )$$

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Increasing in                                                                                        $$(1,\,\,\infty )$$

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Decreasing in                                                                                        $$(1,\,\,\infty )$$

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Increasing in                                                                                              $$(1,\,e),$$  decreasing in                                                                                            $$(e,\infty )$$

1.	The function \[f(x)={{x}^{1/x}}\] is [AMU 2002]
A.	Increasing in \[(1,\,\,\infty )\]
B.	Decreasing in \[(1,\,\,\infty )\]
C.	Increasing in \[(1,\,e),\] decreasing in \[(e,\infty )\]
D.	Decreasing in \[(1,\,e),\] increasing in \[(e,\infty )\]
Answer» D. Decreasing in \[(1,\,e),\] increasing in \[(e,\infty )\]

The function \[f(x)={{x}^{1/x}}\] is [AMU 2002]

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