What is the extreme x/(x^2+2) ?

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

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extreme x/(x^2+2)

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

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

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

Plug

x = 2

into

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

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

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

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