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Beliebt Funktionen >

extreme f(x)=-x^3+6x^2-9x-1

Lösung

extrempunkte

f (x) = - x^{3} + 6 x^{2} - 9 x - 1

Lösung

Minimum (1, - 5), Maximum (3, - 1)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 12 x - 9

Intervalle finden:

Absteigend

: - \infty < x < 1,

Ansteigend

: 1 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = 1

in

- x^{3} + 6 x^{2} - 9 x - 1 : - 5

Minimum (1, - 5)

Stecke

x = 3

in

- x^{3} + 6 x^{2} - 9 x - 1 : - 1

Maximum (3, - 1)

Minimum (1, - 5), Maximum (3, - 1)

Graph

Beliebte Beispiele

extreme f(x)=(-1/100 (x)(x-300))

e x t re m e f (x) = (- \frac{1}{100} (x) (x - 300))

extreme f(x)=2x+6,-4<= x<= 2

e x t re m e f (x) = 2 x + 6, - 4 \leq x \leq 2

extreme f(x)=(x-9)^3

e x t re m e f (x) = (x - 9)^{3}

extreme f(x)=1-x^{4/5}

e x t re m e f (x) = 1 - x^{\frac{4}{5}}

extreme f(x)=4+5x+x^2

e x t re m e f (x) = 4 + 5 x + x^{2}