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Beliebt Funktionen >

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

Lösung

extrempunkte

\frac{x ^{3}}{x ^{2} + x - 2}

Lösung

Maximum (- 1 - 7, - \frac{2 ( 10 + 7 7 )}{9}), Sattel (0, 0), Minimum (- 1 + 7, \frac{2 ( 7 7 - 10 )}{9})

Schritte zur Lösung

f^{'} (x) = \frac{x ^{4} + 2 x ^{3} - 6 x ^{2}}{( x ^{2} + x - 2 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - 1 - 7,

Absteigend

: - 1 - 7 < x < - 2,

Absteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 1,

Absteigend

: 1 < x < - 1 + 7,

Ansteigend

: - 1 + 7 < x < \infty

Stecke

x = - 1 - 7

in

\frac{x ^{3}}{x ^{2} + x - 2} : - \frac{2 ( 10 + 7 7 )}{9}

Maximum (- 1 - 7, - \frac{2 ( 10 + 7 7 )}{9})

Stecke

x = 0

in

\frac{x ^{3}}{x ^{2} + x - 2} : 0

Sattel (0, 0)

Stecke

x = - 1 + 7

in

\frac{x ^{3}}{x ^{2} + x - 2} : \frac{2 ( 7 7 - 10 )}{9}

Minimum (- 1 + 7, \frac{2 ( 7 7 - 10 )}{9})

Maximum (- 1 - 7, - \frac{2 ( 10 + 7 7 )}{9}), Sattel (0, 0), Minimum (- 1 + 7, \frac{2 ( 7 7 - 10 )}{9})

Graph

Beliebte Beispiele

extreme f(x)=x^4+18x^2+5,-6<= x<= 6

e x t re m e f (x) = x^{4} + 18 x^{2} + 5, - 6 \leq x \leq 6

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

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

extreme f(x)=(x^2-4y^2)e^{1-x^2-y^2}

e x t re m e f (x) = (x^{2} - 4 y^{2}) e^{1 - x^{2} - y^{2}}

extreme f(x,y)=x^3-3x+y^2-y^4

e x t re m e f (x, y) = x^{3} - 3 x + y^{2} - y^{4}

extreme f(x)=(x-10)^{1/3}

e x t re m e f (x) = (x - 10)^{\frac{1}{3}}