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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (- 1, 0), Minimum (\frac{1}{3}, - \frac{32}{27})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < \frac{1}{3},

Ansteigend

: \frac{1}{3} < x < \infty

Stecke

x = - 1

in

x^{3} + x^{2} - x - 1 : 0

Maximum (- 1, 0)

Stecke

x = \frac{1}{3}

in

x^{3} + x^{2} - x - 1 : - \frac{32}{27}

Minimum (\frac{1}{3}, - \frac{32}{27})

Maximum (- 1, 0), Minimum (\frac{1}{3}, - \frac{32}{27})

Graph

Beliebte Beispiele

extreme f(x)=(x^2+10)(9-x^2)

e x t re m e f (x) = (x^{2} + 10) (9 - x^{2})

extreme f(x,y)=3x^4+3y^4-xy

e x t re m e f (x, y) = 3 x^{4} + 3 y^{4} - x y

extreme (4x^2)/(x^2-4)

e x t re m e \frac{4 x ^{2}}{x ^{2} - 4}

extreme f(x)=2x^3-21x^2+60x,0<= x<= 6

e x t re m e f (x) = 2 x^{3} - 21 x^{2} + 60 x, 0 \leq x \leq 6

extreme f(x,y)=x^2-xy+y^2

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