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Beliebt Funktionen >

extreme f(x)= 1/4 x^2+x^3-2

Lösung

extrempunkte

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

Lösung

Maximum (- \frac{1}{6}, - \frac{863}{432}), Minimum (0, - 2)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1}{6},

Absteigend

: - \frac{1}{6} < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - \frac{1}{6}

in

\frac{1}{4} x^{2} + x^{3} - 2 : - \frac{863}{432}

Maximum (- \frac{1}{6}, - \frac{863}{432})

Stecke

x = 0

in

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

Minimum (0, - 2)

Maximum (- \frac{1}{6}, - \frac{863}{432}), Minimum (0, - 2)

Graph

Beliebte Beispiele

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

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

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

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

extreme f(x)=4x^5-60x^3

e x t re m e f (x) = 4 x^{5} - 60 x^{3}

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

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

extreme 3x^2-18x+15

e x t re m e 3 x^{2} - 18 x + 15