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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (- 2, - 2), Maximum (0, \frac{2}{3}), Minimum (1, \frac{1}{4})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 2

in

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

Minimum (- 2, - 2)

Stecke

x = 0

in

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

Maximum (0, \frac{2}{3})

Stecke

x = 1

in

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

Minimum (1, \frac{1}{4})

Minimum (- 2, - 2), Maximum (0, \frac{2}{3}), Minimum (1, \frac{1}{4})

Graph

Beliebte Beispiele

extreme f(x,y)=-4*(x^2+6x+8)/(y^2+6y+6)

e x t re m e f (x, y) = - 4 \cdot \frac{x ^{2} + 6 x + 8}{y ^{2} + 6 y + 6}

extreme f(x)=x+(108)/(x^2)

e x t re m e f (x) = x + \frac{108}{x ^{2}}

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

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

extreme g(x,y)=xy^{1/2}

e x t re m e g (x, y) = x y^{\frac{1}{2}}

extreme f(x)=x^3-6x^2+12x-5

e x t re m e f (x) = x^{3} - 6 x^{2} + 12 x - 5