What is the extreme f(x)=xe^{1/x} ?

The extreme f(x)=xe^{1/x} is Minimum(1,e)

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extreme f(x)=xe^{1/x}

extreme

Minimum (1, e)

Solution steps

Find the critical points:

x = 1

Domain of

x e^{\frac{1}{x}} : x < 0 or x > 0

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug the extreme point

x = 1

into

x e^{\frac{1}{x}} \Rightarrow y = e

Minimum (1, e)