What is the extreme f(x)=3+x+9/x ,(0,infinity) ?

The extreme f(x)=3+x+9/x ,(0,infinity) is Minimum(3,9)

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extreme f(x)=3+x+9/x ,(0,infinity)

extreme points

f (x) = 3 + x + \frac{9}{x}, (0, \infty)

Minimum (3, 9)

Solution steps

Find the critical points:

x = 3

Domain of

3 + x + \frac{9}{x}, (0, \infty) : x > 0

Find intervals:

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug the extreme point

x = 3

into

3 + x + \frac{9}{x} \Rightarrow y = 9

Minimum (3, 9)

f (x) = x^{\frac{2}{9}} (7 x + 11)

3 x + \frac{75}{x}

x^{2} - y^{2} - 6 x + 6 y + 2

\frac{2 x ^{2} - 8}{- x ^{2} - 2 x + 3}

f (x) = 6 x - \frac{1}{7 x}

What is the extreme f(x)=3+x+9/x ,(0,infinity) ?
The extreme f(x)=3+x+9/x ,(0,infinity) is Minimum(3,9)