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

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

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extreme f(x)=x+7/x

extreme points

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

Maximum (- 7, - 27), Minimum (7, 27)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 7,

Decreasing

: - 7 < x < 0,

Decreasing

: 0 < x < 7,

Increasing

: 7 < x < \infty

Plug

x = - 7

into

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

Maximum (- 7, - 27)

Plug

x = 7

into

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

Minimum (7, 27)

Maximum (- 7, - 27), Minimum (7, 27)

\frac{4 x}{x ^{2} + 1}

- \frac{2}{x ^{2} - 4}

f (x, y) = x y + \frac{4}{x} + \frac{2}{y}

f (x) = \frac{2}{x ^{2} + 3}

f (x) = x^{2} (x^{2} - 1)

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