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Beliebt Funktionen >

extreme f(x)=-3x^4+20x^3-36x^2+7

Lösung

extrempunkte

f (x) = - 3 x^{4} + 20 x^{3} - 36 x^{2} + 7

Lösung

Maximum (0, 7), Minimum (2, - 25), Maximum (3, - 20)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = 0

in

- 3 x^{4} + 20 x^{3} - 36 x^{2} + 7 : 7

Maximum (0, 7)

Stecke

x = 2

in

- 3 x^{4} + 20 x^{3} - 36 x^{2} + 7 : - 25

Minimum (2, - 25)

Stecke

x = 3

in

- 3 x^{4} + 20 x^{3} - 36 x^{2} + 7 : - 20

Maximum (3, - 20)

Maximum (0, 7), Minimum (2, - 25), Maximum (3, - 20)

Graph

Beliebte Beispiele

extreme y=-2+5sin(pi/(12)(x-2))

e x t re m e y = - 2 + 5 sin (\frac{π}{12} (x - 2))

extreme (x^2-1)(x^2-9)

e x t re m e (x^{2} - 1) (x^{2} - 9)

extreme y=(25/32 x^3+6400)/x

e x t re m e y = \frac{\frac{25}{32} x ^{3} + 6400}{x}

extreme f(x)=x|x|

e x t re m e f (x) = x ∣ x ∣

extreme E(x)=x^4-8x+3x^2+xm-5-11

e x t re m e E (x) = x^{4} - 8 x + 3 x^{2} + x m - 5 - 11