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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (\frac{1}{5}, \frac{256}{3125}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = (x - 1)^{3} (5 x - 1)

Intervalle finden:

Ansteigend

: - \infty < x < \frac{1}{5},

Absteigend

: \frac{1}{5} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = \frac{1}{5}

in

x (1 - x)^{4} : \frac{256}{3125}

Maximum (\frac{1}{5}, \frac{256}{3125})

Stecke

x = 1

in

x (1 - x)^{4} : 0

Minimum (1, 0)

Maximum (\frac{1}{5}, \frac{256}{3125}), Minimum (1, 0)

Graph

Beliebte Beispiele

extreme x^4-2x^2+2

e x t re m e x^{4} - 2 x^{2} + 2

extreme f(x)=e^{-3x^2}

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

extreme f(x,y)=e^{5xy}

e x t re m e f (x, y) = e^{5 x y}

extreme f(x,y)=2x+2y

e x t re m e f (x, y) = 2 x + 2 y

extreme f(s,t)=s^3-2t^2+8st

e x t re m e f (s, t) = s^{3} - 2 t^{2} + 8 s t