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Beliebt Funktionen >

extreme x^4+(1-x)^4+10x^2(1-x)^2

Lösung

extrempunkte

x^{4} + (1 - x)^{4} + 10 x^{2} (1 - x)^{2}

Lösung

Minimum (\frac{3 - 3}{6}, \frac{2}{3}), Maximum (\frac{1}{2}, \frac{3}{4}), Minimum (\frac{3 + 3}{6}, \frac{2}{3})

Schritte zur Lösung

f^{'} (x) = 48 x^{3} - 72 x^{2} + 32 x - 4

Intervalle finden:

Absteigend

: - \infty < x < \frac{3 - 1}{2 3},

Ansteigend

: \frac{3 - 1}{2 3} < x < \frac{1}{2},

Absteigend

: \frac{1}{2} < x < \frac{1 + 3}{2 3},

Ansteigend

: \frac{1 + 3}{2 3} < x < \infty

Stecke

x = \frac{3 - 3}{6}

in

x^{4} + (1 - x)^{4} + 10 x^{2} (1 - x)^{2} : \frac{2}{3}

Minimum (\frac{3 - 3}{6}, \frac{2}{3})

Stecke

x = \frac{1}{2}

in

x^{4} + (1 - x)^{4} + 10 x^{2} (1 - x)^{2} : \frac{3}{4}

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

Stecke

x = \frac{3 + 3}{6}

in

x^{4} + (1 - x)^{4} + 10 x^{2} (1 - x)^{2} : \frac{2}{3}

Minimum (\frac{3 + 3}{6}, \frac{2}{3})

Minimum (\frac{3 - 3}{6}, \frac{2}{3}), Maximum (\frac{1}{2}, \frac{3}{4}), Minimum (\frac{3 + 3}{6}, \frac{2}{3})

Graph

Beliebte Beispiele

e x t re m e - 7 x + 6

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

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

extreme f(x)=cos(x)-5x

e x t re m e f (x) = cos (x) - 5 x

extreme y=(x^2)/(x-1)

e x t re m e y = \frac{x ^{2}}{x - 1}

extreme f(x)=cos(x)-6x

e x t re m e f (x) = cos (x) - 6 x