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)

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 17

x^{2} - 6 x + 7

f (x) = x^{3} + 6 x^{2} + 9 x - 8

f (x, y) = x^{3} - y^{3} - 2 x y + 10

f (x) = 2 x^{2} - 8 x, 0 \leq x \leq 6

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)