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Beliebt Funktionen >

extreme f(x)=3x^4+20x^3-36x^2-4

Lösung

extrempunkte

f (x) = 3 x^{4} + 20 x^{3} - 36 x^{2} - 4

Lösung

Minimum (- 6, - 1732), Maximum (0, - 4), Minimum (1, - 17)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} + 60 x^{2} - 72 x

Intervalle finden:

Absteigend

: - \infty < x < - 6,

Ansteigend

: - 6 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 6

in

3 x^{4} + 20 x^{3} - 36 x^{2} - 4 : - 1732

Minimum (- 6, - 1732)

Stecke

x = 0

in

3 x^{4} + 20 x^{3} - 36 x^{2} - 4 : - 4

Maximum (0, - 4)

Stecke

x = 1

in

3 x^{4} + 20 x^{3} - 36 x^{2} - 4 : - 17

Minimum (1, - 17)

Minimum (- 6, - 1732), Maximum (0, - 4), Minimum (1, - 17)

Graph

Beliebte Beispiele

extreme 2x^3-30x^2,-1<= x<= 11

e x t re m e 2 x^{3} - 30 x^{2}, - 1 \leq x \leq 11

extreme f(x)=x(1-x)^{2/5}

e x t re m e f (x) = x (1 - x)^{\frac{2}{5}}

extreme f(x)=sqrt(x^2-2x+2),-2<= x<= 2

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

extreme 6/(-3x+2)

e x t re m e \frac{6}{- 3 x + 2}

extreme ln(x^2-4)

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