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

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

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

extreme points

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

Maximum (- 2, - 2), Minimum (2, 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, - 2)

Plug

x = 2

into

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

Minimum (2, 2)

Maximum (- 2, - 2), Minimum (2, 2)

f (x) = x^{\frac{3}{2}} - x^{\frac{1}{2}}, 0 \leq x \leq 1

f (x) = - \frac{1}{4} x^{4} + x^{3} + 5

f (x) = x^{2} + 8 x + 16

f (x) = e^{2 x}

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

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