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

Lösung

extrempunkte

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

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

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

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

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

Stecke

x = 3

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

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

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

e x t re m e f (x) = x 9 - x^{2}, - 3 \leq x \leq 3

e x t re m e f (x) = \frac{x ^{2} + 3}{x ^{3} - 9}

e x t re m e f (x, y) = (x - y) (4 - x y)

e x t re m e x^{4} - x^{3}

e x t re m e x^{6} (x - 4)^{5}