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Beliebt Funktionen >

extreme f(x)=x^4-12x^3+4

Lösung

extrempunkte

f (x) = x^{4} - 12 x^{3} + 4

Lösung

Sattel (0, 4), Minimum (9, - 2183)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 36 x^{2}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 9,

Ansteigend

: 9 < x < \infty

Stecke

x = 0

in

x^{4} - 12 x^{3} + 4 : 4

Sattel (0, 4)

Stecke

x = 9

in

x^{4} - 12 x^{3} + 4 : - 2183

Minimum (9, - 2183)

Sattel (0, 4), Minimum (9, - 2183)

Graph

Beliebte Beispiele

extreme f(x)=2x^3+45x^2-300x,4<= x<= 11

e x t re m e f (x) = 2 x^{3} + 45 x^{2} - 300 x, 4 \leq x \leq 11

extreme f(x)=2x^4-x^2

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

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

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

extreme p(x)=12x^4+15x^3+ax^2-69x-30

e x t re m e p (x) = 12 x^{4} + 15 x^{3} + a x^{2} - 69 x - 30

extreme f(x,y)=x+2 y/2 x+y

e x t re m e f (x, y) = x + 2 \frac{y}{2} x + y