What is the extreme f(x)= x/(5+x^2) ?

The extreme f(x)= x/(5+x^2) is Minimum(-sqrt(5),-1/(2sqrt(5))),Maximum(sqrt(5), 1/(2sqrt(5)))

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extreme f(x)= x/(5+x^2)

extreme points

f (x) = \frac{x}{5 + x ^{2}}

Minimum (- 5, - \frac{1}{2 5}), Maximum (5, \frac{1}{2 5})

Solution steps

f^{'} (x) = \frac{5 - x ^{2}}{( 5 + x ^{2} ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 5

into

\frac{x}{5 + x ^{2}} : - \frac{1}{2 5}

Minimum (- 5, - \frac{1}{2 5})

Plug

x = 5

into

\frac{x}{5 + x ^{2}} : \frac{1}{2 5}

Maximum (5, \frac{1}{2 5})

Minimum (- 5, - \frac{1}{2 5}), Maximum (5, \frac{1}{2 5})

9 x + 4 y = - 3

\frac{x}{x ^{2} - 4}

f (x) = 6 tan (0.2 x)

\frac{3 x}{7 x - 1}

4 sin^{2} (x)

What is the extreme f(x)= x/(5+x^2) ?
The extreme f(x)= x/(5+x^2) is Minimum(-sqrt(5),-1/(2sqrt(5))),Maximum(sqrt(5), 1/(2sqrt(5)))