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Beliebt Funktionen >

extreme y=x^4-8x^2+3

Lösung

extrempunkte

y = x^{4} - 8 x^{2} + 3

Lösung

Minimum (- 2, - 13), Maximum (0, 3), Minimum (2, - 13)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 16 x

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

in

x^{4} - 8 x^{2} + 3 : - 13

Minimum (- 2, - 13)

Stecke

x = 0

in

x^{4} - 8 x^{2} + 3 : 3

Maximum (0, 3)

Stecke

x = 2

in

x^{4} - 8 x^{2} + 3 : - 13

Minimum (2, - 13)

Minimum (- 2, - 13), Maximum (0, 3), Minimum (2, - 13)

Graph

Beliebte Beispiele

extreme f(x)=x^{4/5}(x-9)^2

e x t re m e f (x) = x^{\frac{4}{5}} (x - 9)^{2}

extreme 1/4 x+3

e x t re m e \frac{1}{4} x + 3

extreme f(x,y)=ye^x

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

extreme f(x)=x^3+18x^2+81x

e x t re m e f (x) = x^{3} + 18 x^{2} + 81 x

extreme f(x)=5-2x^2

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