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Beliebt Funktionen >

extreme f(x)=3x^4+4x^3-120x^2+120

Lösung

extrempunkte

f (x) = 3 x^{4} + 4 x^{3} - 120 x^{2} + 120

Lösung

Minimum (- 5, - 1505), Maximum (0, 120), Minimum (4, - 776)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} + 12 x^{2} - 240 x

Intervalle finden:

Absteigend

: - \infty < x < - 5,

Ansteigend

: - 5 < x < 0,

Absteigend

: 0 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = - 5

in

3 x^{4} + 4 x^{3} - 120 x^{2} + 120 : - 1505

Minimum (- 5, - 1505)

Stecke

x = 0

in

3 x^{4} + 4 x^{3} - 120 x^{2} + 120 : 120

Maximum (0, 120)

Stecke

x = 4

in

3 x^{4} + 4 x^{3} - 120 x^{2} + 120 : - 776

Minimum (4, - 776)

Minimum (- 5, - 1505), Maximum (0, 120), Minimum (4, - 776)

Graph

Beliebte Beispiele

extreme f(x)=14x^2-7x^4

e x t re m e f (x) = 14 x^{2} - 7 x^{4}

extreme f(x)=30x^4-13x^3-54x^2-1

e x t re m e f (x) = 30 x^{4} - 13 x^{3} - 54 x^{2} - 1

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

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

extreme f(x)=8-x,-1<= x<= 3

e x t re m e f (x) = 8 - x, - 1 \leq x \leq 3

extreme P(x,y)=x^2+5xy-4y^2

e x t re m e P (x, y) = x^{2} + 5 x y - 4 y^{2}