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Beliebt Funktionen >

extreme (x^4)/(x^2-1)

Lösung

extrempunkte

\frac{x ^{4}}{x ^{2} - 1}

Lösung

Minimum (- 2, 4), Maximum (0, 0), Minimum (2, 4)

Schritte zur Lösung

f^{'} (x) = \frac{2 x ^{5} - 4 x ^{3}}{( x ^{2} - 1 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Absteigend

: 1 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

in

\frac{x ^{4}}{x ^{2} - 1} : 4

Minimum (- 2, 4)

Stecke

x = 0

in

\frac{x ^{4}}{x ^{2} - 1} : 0

Maximum (0, 0)

Stecke

x = 2

in

\frac{x ^{4}}{x ^{2} - 1} : 4

Minimum (2, 4)

Minimum (- 2, 4), Maximum (0, 0), Minimum (2, 4)

Graph

Beliebte Beispiele

extreme f(x,y)=3sqrt(16-x^2-y^2)

e x t re m e f (x, y) = 3 16 - x^{2} - y^{2}

extreme f(x)=(2x^2)/(x-2),-2<= x<= 1

e x t re m e f (x) = \frac{2 x ^{2}}{x - 2}, - 2 \leq x \leq 1

extreme x^3-x^2-8x+8

e x t re m e x^{3} - x^{2} - 8 x + 8

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

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

extreme f(x)=4x^2-32ln(x)

e x t re m e f (x) = 4 x^{2} - 32 ln (x)