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Beliebt Funktionen >

extreme f(x)=(x+1)^{2/3}(x-3)^2

Lösung

extrempunkte

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

Lösung

Minimum (- 1, 0), Maximum (0, 9), Minimum (3, 0)

Schritte zur Lösung

f^{'} (x) = \frac{8 x ( - 3 + x )}{3 ( 1 + x ) ^{\frac{1}{3}}}

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 1

in

(x + 1)^{\frac{2}{3}} (x - 3)^{2} : 0

Minimum (- 1, 0)

Stecke

x = 0

in

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

Maximum (0, 9)

Stecke

x = 3

in

(x + 1)^{\frac{2}{3}} (x - 3)^{2} : 0

Minimum (3, 0)

Minimum (- 1, 0), Maximum (0, 9), Minimum (3, 0)

Graph

Beliebte Beispiele

extreme f(x)= 1/4 x^4+4/3 x^3+2x^2

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

extreme f(x)=(1-x^2)^2

e x t re m e f (x) = (1 - x^{2})^{2}

extreme f(x,y)=2xy+x^2y-y

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

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

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

extreme f(x)=x^2-4xy+y^3+4y

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