What is the monotone xe^{1/x} ?

The monotone xe^{1/x} is Increasing:-infinity <x<0,Decreasing:0<x<1,Increasing:1<x<infinity

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monotone xe^{1/x}

monotone intervals

x e^{\frac{1}{x}}

Increasing : - \infty < x < 0, Decreasing : 0 < x < 1, Increasing : 1 < x < \infty

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

Increasing : - \infty < x < 0, Decreasing : 0 < x < 1, Increasing : 1 < x < \infty

\frac{4 x ^{2} + 4 x + 1}{2 x ^{3} + 8 x ^{2}}

(8, 1), (- 2, - 5)

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

x^{2} + 16

f (x) = \frac{5}{x - 9}

What is the monotone xe^{1/x} ?
The monotone xe^{1/x} is Increasing:-infinity <x<0,Decreasing:0<x<1,Increasing:1<x<infinity