What is the extreme f(x)=3-x-2/x ?

The extreme f(x)=3-x-2/x is Minimum(-sqrt(2),3+2sqrt(2)),Maximum(sqrt(2),3-2sqrt(2))

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extreme f(x)=3-x-2/x

extreme points

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

Minimum (- 2, 3 + 22), Maximum (2, 3 - 22)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

3 - x - \frac{2}{x} : 3 + 22

Minimum (- 2, 3 + 22)

Plug

x = 2

into

3 - x - \frac{2}{x} : 3 - 22

Maximum (2, 3 - 22)

Minimum (- 2, 3 + 22), Maximum (2, 3 - 22)

What is the extreme f(x)=3-x-2/x ?
The extreme f(x)=3-x-2/x is Minimum(-sqrt(2),3+2sqrt(2)),Maximum(sqrt(2),3-2sqrt(2))