What is the extreme f(x)=x+(25)/x ?

The extreme f(x)=x+(25)/x is Maximum(-5,-10),Minimum(5,10)

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extreme f(x)=x+(25)/x

extreme

Maximum (- 5, - 10), Minimum (5, 10)

Solution steps

f^{'} (x) = 1 - \frac{25}{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{25}{x} : - 10

Maximum (- 5, - 10)

Plug

x = 5

into

x + \frac{25}{x} : 10

Minimum (5, 10)

Maximum (- 5, - 10), Minimum (5, 10)

What is the extreme f(x)=x+(25)/x ?
The extreme f(x)=x+(25)/x is Maximum(-5,-10),Minimum(5,10)