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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (- 1, - \frac{3}{2}), Maximum (0, - 1), Minimum (1, - \frac{3}{2})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

in

\frac{1}{2} x^{4} - x^{2} - 1 : - \frac{3}{2}

Minimum (- 1, - \frac{3}{2})

Stecke

x = 0

in

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

Maximum (0, - 1)

Stecke

x = 1

in

\frac{1}{2} x^{4} - x^{2} - 1 : - \frac{3}{2}

Minimum (1, - \frac{3}{2})

Minimum (- 1, - \frac{3}{2}), Maximum (0, - 1), Minimum (1, - \frac{3}{2})

Graph

Beliebte Beispiele

extreme f(x)=3+9x^2-6x^3

e x t re m e f (x) = 3 + 9 x^{2} - 6 x^{3}

extreme f(x,y)=xe^{-x^2-y^2}

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

extreme f(x)=arcos(1-|x|)-pi

e x t re m e f (x) = a r cos (1 - ∣ x ∣) - π

extreme f(x,y)=7xy

e x t re m e f (x, y) = 7 x y

extreme f(x,y)=x^2-6xy+9y^2+3x-10

e x t re m e f (x, y) = x^{2} - 6 x y + 9 y^{2} + 3 x - 10