What is the extreme f(x)=2x+1/x ?

The extreme f(x)=2x+1/x is Maximum(-1/(sqrt(2)),-2sqrt(2)),Minimum(1/(sqrt(2)),2sqrt(2))

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extreme f(x)=2x+1/x

extreme points

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

Maximum (- \frac{1}{2}, - 22), Minimum (\frac{1}{2}, 22)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < 0,

Decreasing

: 0 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

2 x + \frac{1}{x} : - 22

Maximum (- \frac{1}{2}, - 22)

Plug

x = \frac{1}{2}

into

2 x + \frac{1}{x} : 22

Minimum (\frac{1}{2}, 22)

Maximum (- \frac{1}{2}, - 22), Minimum (\frac{1}{2}, 22)

What is the extreme f(x)=2x+1/x ?
The extreme f(x)=2x+1/x is Maximum(-1/(sqrt(2)),-2sqrt(2)),Minimum(1/(sqrt(2)),2sqrt(2))