What is the extreme f(x)=7x+1/x ?

The extreme f(x)=7x+1/x is Maximum(-1/(sqrt(7)),-2sqrt(7)),Minimum(1/(sqrt(7)),2sqrt(7))

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extreme f(x)=7x+1/x

extreme points

f (x) = 7 x + \frac{1}{x}

Maximum (- \frac{1}{7}, - 27), Minimum (\frac{1}{7}, 27)

Solution steps

f^{'} (x) = 7 - \frac{1}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{1}{7},

Decreasing

: - \frac{1}{7} < x < 0,

Decreasing

: 0 < x < \frac{1}{7},

Increasing

: \frac{1}{7} < x < \infty

Plug

x = - \frac{1}{7}

into

7 x + \frac{1}{x} : - 27

Maximum (- \frac{1}{7}, - 27)

Plug

x = \frac{1}{7}

into

7 x + \frac{1}{x} : 27

Minimum (\frac{1}{7}, 27)

Maximum (- \frac{1}{7}, - 27), Minimum (\frac{1}{7}, 27)

x, y = - \frac{1}{2} f x_{+ 1}

5 cos (x)

f (x) = \frac{3}{5} (x^{2} - 1)^{\frac{2}{3}}

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

What is the extreme f(x)=7x+1/x ?
The extreme f(x)=7x+1/x is Maximum(-1/(sqrt(7)),-2sqrt(7)),Minimum(1/(sqrt(7)),2sqrt(7))