What is the extreme f(x)=3x+1/x ?

The extreme f(x)=3x+1/x is Maximum(-1/(sqrt(3)),-2sqrt(3)),Minimum(1/(sqrt(3)),2sqrt(3))

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extreme f(x)=3x+1/x

extreme points

f (x) = 3 x + \frac{1}{x}

Maximum (- \frac{1}{3}, - 23), Minimum (\frac{1}{3}, 23)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{3},

Decreasing

: - \frac{1}{3} < x < 0,

Decreasing

: 0 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

3 x + \frac{1}{x} : - 23

Maximum (- \frac{1}{3}, - 23)

Plug

x = \frac{1}{3}

into

3 x + \frac{1}{x} : 23

Minimum (\frac{1}{3}, 23)

Maximum (- \frac{1}{3}, - 23), Minimum (\frac{1}{3}, 23)

f (x) = x^{3} - 15 x^{2} + 48 x + 2

\frac{x ^{2} - 5}{x + 3}

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

- x^{2} ln (x)

f (x) = \frac{3}{4 x ^{4} - 8 x ^{2}}

What is the extreme f(x)=3x+1/x ?
The extreme f(x)=3x+1/x is Maximum(-1/(sqrt(3)),-2sqrt(3)),Minimum(1/(sqrt(3)),2sqrt(3))