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Beliebt Funktionen >

extreme f(x)=x^4-3x^2=x^2(x^2-3)

Lösung

extrempunkte

f (x) = x^{4} - 3 x^{2} = x^{2} (x^{2} - 3)

Lösung

Minimum (- \frac{3}{2}, - \frac{9}{4}), Maximum (0, 0), Minimum (\frac{3}{2}, - \frac{9}{4})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - \frac{3}{2},

Ansteigend

: - \frac{3}{2} < x < 0,

Absteigend

: 0 < x < \frac{3}{2},

Ansteigend

: \frac{3}{2} < x < \infty

Stecke

x = - \frac{3}{2}

in

x^{2} (x^{2} - 3) : - \frac{9}{4}

Minimum (- \frac{3}{2}, - \frac{9}{4})

Stecke

x = 0

in

x^{2} (x^{2} - 3) : 0

Maximum (0, 0)

Stecke

x = \frac{3}{2}

in

x^{2} (x^{2} - 3) : - \frac{9}{4}

Minimum (\frac{3}{2}, - \frac{9}{4})

Minimum (- \frac{3}{2}, - \frac{9}{4}), Maximum (0, 0), Minimum (\frac{3}{2}, - \frac{9}{4})

Graph

Beliebte Beispiele

extreme g(x,y)=x^3+y^3-3x-3y

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

extreme f(x)=-x^6-3x^3+x+1

e x t re m e f (x) = - x^{6} - 3 x^{3} + x + 1

x^{2} = - 4 a y

extreme f(x)=3sin(x)cos(x)

e x t re m e f (x) = 3 sin (x) cos (x)

extreme f(x)=4x-y

e x t re m e f (x) = 4 x - y