What is the extreme f(x)= x/(9+x^2) ?

The extreme f(x)= x/(9+x^2) is Minimum(-3,-1/6),Maximum(3, 1/6)

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extreme f(x)= x/(9+x^2)

extreme points

f (x) = \frac{x}{9 + x ^{2}}

Minimum (- 3, - \frac{1}{6}), Maximum (3, \frac{1}{6})

Solution steps

f^{'} (x) = \frac{9 - x ^{2}}{( 9 + x ^{2} ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

\frac{x}{9 + x ^{2}} : - \frac{1}{6}

Minimum (- 3, - \frac{1}{6})

Plug

x = 3

into

\frac{x}{9 + x ^{2}} : \frac{1}{6}

Maximum (3, \frac{1}{6})

Minimum (- 3, - \frac{1}{6}), Maximum (3, \frac{1}{6})

f (x, y) = x^{2} + y^{3} - 6 x y + 3 x + 6 y - 2

f (x) = 2 x^{3} + 9 x^{2} - 24 x

f (x, y) = 2 x^{2} - 4 x + y^{2} - 8 y + 1

f (x) = \frac{x ^{3}}{3} - 6 x^{2}

f (x) = - x^{3} + 12 x - 14

What is the extreme f(x)= x/(9+x^2) ?
The extreme f(x)= x/(9+x^2) is Minimum(-3,-1/6),Maximum(3, 1/6)