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

Lösung

extrempunkte

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

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

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 3

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

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

Stecke

x = 3

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

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

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

e x t re m e f (x) = x^{2} - 4, - 3 \leq x \leq 2

e x t re m e f (x) = (7.8 x^{2} - 225 x + 1709)

e x t re m e f (x) = - 2 x^{3} - 2 y^{3} + 6 x y + 10

e x t re m e f (x) = 3 x^{2} - 2 x + y^{2} - 4 y + 1

e x t re m e y = x^{2} - 2 ln (x)