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Beliebt Funktionen >

extreme f(x)=(x^5)/5-8/3 x^3

Lösung

extrempunkte

f (x) = \frac{x ^{5}}{5} - \frac{8}{3} x^{3}

Lösung

Maximum (- 22, \frac{256 2}{15}), Sattel (0, 0), Minimum (22, - \frac{256 2}{15})

Schritte zur Lösung

f^{'} (x) = x^{4} - 8 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - 22,

Absteigend

: - 22 < x < 0,

Absteigend

: 0 < x < 22,

Ansteigend

: 22 < x < \infty

Stecke

x = - 22

in

\frac{x ^{5}}{5} - \frac{8}{3} x^{3} : \frac{256 2}{15}

Maximum (- 22, \frac{256 2}{15})

Stecke

x = 0

in

\frac{x ^{5}}{5} - \frac{8}{3} x^{3} : 0

Sattel (0, 0)

Stecke

x = 22

in

\frac{x ^{5}}{5} - \frac{8}{3} x^{3} : - \frac{256 2}{15}

Minimum (22, - \frac{256 2}{15})

Maximum (- 22, \frac{256 2}{15}), Sattel (0, 0), Minimum (22, - \frac{256 2}{15})

Graph

Beliebte Beispiele

extreme (4x)/(25-x^2)

e x t re m e \frac{4 x}{25 - x ^{2}}

extreme f(x)=x^{1/5}(x+6)

e x t re m e f (x) = x^{\frac{1}{5}} (x + 6)

extreme f(x)=sqrt(x^2+0.3x)-0.22x

e x t re m e f (x) = x^{2} + 0.3 x - 0.22 x

extreme y=x(3+5z)

e x t re m e y = x (3 + 5 z)

e x t re m e f (x) = 4