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 points

f (x) = x e^{\frac{1}{x}}

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)

f (x) = \frac{9 x - 1}{2 x + 4}

2 x - 9 y - 4 = 0

f (x) = ln (\frac{( ∣ x ∣ - 1 )}{x ^{2} - 2})

f (x) = \frac{3}{x - 13}

2 x^{2} + 5 x + 10