What is the extreme f(x)=x+5/x ?

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

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extreme f(x)=x+5/x

extreme points

f (x) = 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)

y = x 36 - x^{2}

x^{2} - 8 ln (x)

f (x, y) = x y^{2} - 6 x^{2} - 3 x + 2 x y + 9

f (p, q) = pq - \frac{1}{p} - \frac{1}{q}

3 x^{4} - 4 x^{3} - 36 x^{2} + 5

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