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

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

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

extreme points

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

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

Solution steps

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

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

Plug

x = \frac{1}{2}

into

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

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

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

f (x) = x^{2} - 6 x + 1

f (x) = x^{2} - 6 x + 4

(x + 1) (x + 3)

6 sinh (3 x) cosh (3 x)

f (x) = \frac{- 2 ( x ^{2} - 1 )}{x ^{2} - 4}

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