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

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

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extreme y=(-2x)/(9+x^2)

extreme points

y = \frac{- 2 x}{9 + x ^{2}}

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

\frac{- 2 x}{9 + x ^{2}} : \frac{1}{3}

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

Plug

x = 3

into

\frac{- 2 x}{9 + x ^{2}} : - \frac{1}{3}

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

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

f (x) = - x^{2} - 12 x - 27

f (x) = x 9 - x^{2}, - 3 \leq x \leq 3

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

f (x, y) = (x - y) (4 - x y)

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

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