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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (- \frac{5}{2}, - \frac{25}{4}), Maximum (0, 0), Minimum (\frac{5}{2}, - \frac{25}{4})

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 10 x

Intervalle finden:

Absteigend

: - \infty < x < - \frac{5}{2},

Ansteigend

: - \frac{5}{2} < x < 0,

Absteigend

: 0 < x < \frac{5}{2},

Ansteigend

: \frac{5}{2} < x < \infty

Stecke

x = - \frac{5}{2}

in

x^{4} - 5 x^{2} : - \frac{25}{4}

Minimum (- \frac{5}{2}, - \frac{25}{4})

Stecke

x = 0

in

x^{4} - 5 x^{2} : 0

Maximum (0, 0)

Stecke

x = \frac{5}{2}

in

x^{4} - 5 x^{2} : - \frac{25}{4}

Minimum (\frac{5}{2}, - \frac{25}{4})

Minimum (- \frac{5}{2}, - \frac{25}{4}), Maximum (0, 0), Minimum (\frac{5}{2}, - \frac{25}{4})

Graph

Beliebte Beispiele

extreme f(x)=-1/3 x^3+2x^2-3x-12

e x t re m e f (x) = - \frac{1}{3} x^{3} + 2 x^{2} - 3 x - 12

extreme f(x,y)=2x^4+y^2-16xy

e x t re m e f (x, y) = 2 x^{4} + y^{2} - 16 x y

extreme f(x,y)=2x^3+xy^2+5x^2+y^2+4

e x t re m e f (x, y) = 2 x^{3} + x y^{2} + 5 x^{2} + y^{2} + 4

extreme f(x)=\sqrt[3]{x^2-4}

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

extreme f(x)=6x^4-4x^6

e x t re m e f (x) = 6 x^{4} - 4 x^{6}