What is the extreme f(x)= x/(81+x^2) ?

The extreme f(x)= x/(81+x^2) is Minimum(-9,-1/18),Maximum(9, 1/18)

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extreme f(x)= x/(81+x^2)

extreme points

f (x) = \frac{x}{81 + x ^{2}}

Minimum (- 9, - \frac{1}{18}), Maximum (9, \frac{1}{18})

Solution steps

f^{'} (x) = \frac{81 - x ^{2}}{( 81 + x ^{2} ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 9,

Increasing

: - 9 < x < 9,

Decreasing

: 9 < x < \infty

Plug

x = - 9

into

\frac{x}{81 + x ^{2}} : - \frac{1}{18}

Minimum (- 9, - \frac{1}{18})

Plug

x = 9

into

\frac{x}{81 + x ^{2}} : \frac{1}{18}

Maximum (9, \frac{1}{18})

Minimum (- 9, - \frac{1}{18}), Maximum (9, \frac{1}{18})

f (x) = \frac{x ^{2} - 5}{x - 3}

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

f (x) = - x^{3} + 3 x^{2} - 6, - 2 \leq x \leq 5

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

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

What is the extreme f(x)= x/(81+x^2) ?
The extreme f(x)= x/(81+x^2) is Minimum(-9,-1/18),Maximum(9, 1/18)