What is the extreme f(x)=x+(625)/x ?

The extreme f(x)=x+(625)/x is Maximum(-25,-50),Minimum(25,50)

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extreme f(x)=x+(625)/x

extreme points

f (x) = x + \frac{625}{x}

Maximum (- 25, - 50), Minimum (25, 50)

Solution steps

f^{'} (x) = 1 - \frac{625}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 25,

Decreasing

: - 25 < x < 0,

Decreasing

: 0 < x < 25,

Increasing

: 25 < x < \infty

Plug

x = - 25

into

x + \frac{625}{x} : - 50

Maximum (- 25, - 50)

Plug

x = 25

into

x + \frac{625}{x} : 50

Minimum (25, 50)

Maximum (- 25, - 50), Minimum (25, 50)

What is the extreme f(x)=x+(625)/x ?
The extreme f(x)=x+(625)/x is Maximum(-25,-50),Minimum(25,50)