What is the extreme f(x)=4x+2/x ?

The extreme f(x)=4x+2/x is Maximum(-1/(sqrt(2)),-4sqrt(2)),Minimum(1/(sqrt(2)),4sqrt(2))

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extreme f(x)=4x+2/x

extreme points

f (x) = 4 x + \frac{2}{x}

Maximum (- \frac{1}{2}, - 42), Minimum (\frac{1}{2}, 42)

Solution steps

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

4 x + \frac{2}{x} : - 42

Maximum (- \frac{1}{2}, - 42)

Plug

x = \frac{1}{2}

into

4 x + \frac{2}{x} : 42

Minimum (\frac{1}{2}, 42)

Maximum (- \frac{1}{2}, - 42), Minimum (\frac{1}{2}, 42)

\frac{9}{4} x + 3 y = \frac{9}{4}

∣ x ∣ - 1

y = 1 - x^{2}

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

\frac{x ^{2}}{x ^{2} + x - 2}

What is the extreme f(x)=4x+2/x ?
The extreme f(x)=4x+2/x is Maximum(-1/(sqrt(2)),-4sqrt(2)),Minimum(1/(sqrt(2)),4sqrt(2))