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Beliebt Funktionen >

extreme y=f(x)=x(x-1)^5

Lösung

extrempunkte

y = f (x) = x (x - 1)^{5}

Lösung

Minimum (\frac{1}{6}, - \frac{3125}{46656}), Sattel (1, 0)

Schritte zur Lösung

f^{'} (x) = (x - 1)^{4} (6 x - 1)

Intervalle finden:

Absteigend

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

Ansteigend

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

Ansteigend

: 1 < x < \infty

Stecke

x = \frac{1}{6}

in

x (x - 1)^{5} : - \frac{3125}{46656}

Minimum (\frac{1}{6}, - \frac{3125}{46656})

Stecke

x = 1

in

x (x - 1)^{5} : 0

Sattel (1, 0)

Minimum (\frac{1}{6}, - \frac{3125}{46656}), Sattel (1, 0)

Graph

Beliebte Beispiele

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

e x t re m e y = \frac{e ^{(2 - x)} + x ^{2} - x}{2}

extreme f(x)=20(1+1/x+1/(x^2))

e x t re m e f (x) = 20 (1 + \frac{1}{x} + \frac{1}{x ^{2}})

extreme 2x^2-2xy+y^2-2x

e x t re m e 2 x^{2} - 2 x y + y^{2} - 2 x

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

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

extreme f(x,y)=2x^2+2y^2-16x+12y

e x t re m e f (x, y) = 2 x^{2} + 2 y^{2} - 16 x + 12 y