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Beliebt Funktionen >

extreme f(x)=-x^3+3x^2+9x-27

Lösung

extrempunkte

f (x) = - x^{3} + 3 x^{2} + 9 x - 27

Lösung

Minimum (- 1, - 32), Maximum (3, 0)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 6 x + 9

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 1

in

- x^{3} + 3 x^{2} + 9 x - 27 : - 32

Minimum (- 1, - 32)

Stecke

x = 3

in

- x^{3} + 3 x^{2} + 9 x - 27 : 0

Maximum (3, 0)

Minimum (- 1, - 32), Maximum (3, 0)

Graph

Beliebte Beispiele

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

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

extreme ((x+1))/(x^2-2x-3)

e x t re m e \frac{( x + 1 )}{x ^{2} - 2 x - 3}

extreme f(x)=(x^2+2)/(x^2-9)

e x t re m e f (x) = \frac{x ^{2} + 2}{x ^{2} - 9}

extreme f(x)=(x^3)/3-5x^2-50x+1

e x t re m e f (x) = \frac{x ^{3}}{3} - 5 x^{2} - 50 x + 1

extreme 4/x+x^4

e x t re m e \frac{4}{x} + x^{4}