What is the extreme f(x)=x-1/x+2/(x^3),[0,infinity ] ?

The extreme f(x)=x-1/x+2/(x^3),[0,infinity ] is Minimum(sqrt(2),sqrt(2))

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extreme f(x)=x-1/x+2/(x^3),[0,infinity ]

extreme points

f (x) = x - \frac{1}{x} + \frac{2}{x ^{3}}, [0, \infty]

Minimum (2, 2)

Solution steps

Find the critical points:

x = 2

Domain of

x - \frac{1}{x} + \frac{2}{x ^{3}}, [0, \infty] : x > 0

Find intervals:

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug the extreme point

x = 2

into

x - \frac{1}{x} + \frac{2}{x ^{3}} \Rightarrow y = 2

Minimum (2, 2)

y = 2 x_{1} + 4 x_{2}

f (x, y) = - 25 - x^{2} - y^{2}

f (x) = \frac{x + 5}{x - 3}, (- 5, 2)

f (x) = - \frac{1}{3} x^{3} - x^{2} - 12

f (x) = - \frac{24 x}{x ^{2} + 9}

What is the extreme f(x)=x-1/x+2/(x^3),[0,infinity ] ?
The extreme f(x)=x-1/x+2/(x^3),[0,infinity ] is Minimum(sqrt(2),sqrt(2))