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Beliebt Funktionen >

extreme (x^3)/(x+1)

Lösung

extrempunkte

\frac{x ^{3}}{x + 1}

Lösung

Minimum (- \frac{3}{2}, \frac{27}{4}), Sattel (0, 0)

Schritte zur Lösung

f^{'} (x) = \frac{2 x ^{3} + 3 x ^{2}}{( x + 1 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{3}{2},

Ansteigend

: - \frac{3}{2} < x < - 1,

Ansteigend

: - 1 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - \frac{3}{2}

in

\frac{x ^{3}}{x + 1} : \frac{27}{4}

Minimum (- \frac{3}{2}, \frac{27}{4})

Stecke

x = 0

in

\frac{x ^{3}}{x + 1} : 0

Sattel (0, 0)

Minimum (- \frac{3}{2}, \frac{27}{4}), Sattel (0, 0)

Graph

Beliebte Beispiele

extreme f(x)=x^3+3*x^2-9x+27

e x t re m e f (x) = x^{3} + 3 \cdot x^{2} - 9 x + 27

extreme f(x)=(x^3)/3-4x^2+7x+8

e x t re m e f (x) = \frac{x ^{3}}{3} - 4 x^{2} + 7 x + 8

extreme f(x,y)=ln(1+x^2+y^2)

e x t re m e f (x, y) = ln (1 + x^{2} + y^{2})

extreme f(x)=x-3x^{2/3}

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

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

e x t re m e f (x) = \frac{x ^{5}}{5} - \frac{8}{3} x^{3}