What is the extreme x+5/x ?

The extreme x+5/x is Maximum(-sqrt(5),-2sqrt(5)),Minimum(sqrt(5),2sqrt(5))

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extreme x+5/x

extreme points

x + \frac{5}{x}

Maximum (- 5, - 25), Minimum (5, 25)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

x + \frac{5}{x} : - 25

Maximum (- 5, - 25)

Plug

x = 5

into

x + \frac{5}{x} : 25

Minimum (5, 25)

Maximum (- 5, - 25), Minimum (5, 25)

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

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

(- x^{2} + 4) (x + 1)

4 x - 5 y = 20

(- 3.1, - 2.8), (- 4.92, - 3.3)

What is the extreme x+5/x ?
The extreme x+5/x is Maximum(-sqrt(5),-2sqrt(5)),Minimum(sqrt(5),2sqrt(5))