What is the extreme f(x)=x+1/x ,(0.2,4) ?

The extreme f(x)=x+1/x ,(0.2,4) is Minimum(1,2)

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extreme f(x)=x+1/x ,(0.2,4)

extreme points

f (x) = x + \frac{1}{x}, (0.2, 4)

Minimum (1, 2)

Solution steps

Find the critical points:

x = 1

Domain of

x + \frac{1}{x}, (0.2, 4) : 0.2 < x < 4

Find intervals:

Decreasing

: 0.2 < x < 1,

Increasing

: 1 < x < 4

Plug the extreme point

x = 1

into

x + \frac{1}{x} \Rightarrow y = 2

Minimum (1, 2)

What is the extreme f(x)=x+1/x ,(0.2,4) ?
The extreme f(x)=x+1/x ,(0.2,4) is Minimum(1,2)