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Beliebt Funktionen >

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

Lösung

extrempunkte

f (x) = \frac{x ^{4}}{4} - \frac{4 x ^{3}}{3} + 2 x^{2} - 1

Lösung

Minimum (0, - 1), Sattel (2, \frac{1}{3})

Schritte zur Lösung

f^{'} (x) = x^{3} - 4 x^{2} + 4 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = 0

in

\frac{x ^{4}}{4} - \frac{4 x ^{3}}{3} + 2 x^{2} - 1 : - 1

Minimum (0, - 1)

Stecke

x = 2

in

\frac{x ^{4}}{4} - \frac{4 x ^{3}}{3} + 2 x^{2} - 1 : \frac{1}{3}

Sattel (2, \frac{1}{3})

Minimum (0, - 1), Sattel (2, \frac{1}{3})

Graph

Beliebte Beispiele

extreme-30x^2-25y^2+480x+300y+170

e x t re m e - 30 x^{2} - 25 y^{2} + 480 x + 300 y + 170

extreme f(x)=((x-2)^2)/(x-5)

e x t re m e f (x) = \frac{( x - 2 ) ^{2}}{x - 5}

extreme f(x)=-x^2-5x-2

e x t re m e f (x) = - x^{2} - 5 x - 2

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

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

extreme F(X,Y)=1-X^2+2Y^2

e x t re m e F (X, Y) = 1 - X^{2} + 2 Y^{2}