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Beliebt Funktionen >

extreme f(x)=x^4(1-x)^8

Lösung

extrempunkte

f (x) = x^{4} (1 - x)^{8}

Lösung

Minimum (0, 0), Maximum (\frac{1}{3}, \frac{256}{531441}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} (x - 1)^{7} (3 x - 1)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{1}{3},

Absteigend

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

Ansteigend

: 1 < x < \infty

Stecke

x = 0

in

x^{4} (1 - x)^{8} : 0

Minimum (0, 0)

Stecke

x = \frac{1}{3}

in

x^{4} (1 - x)^{8} : \frac{256}{531441}

Maximum (\frac{1}{3}, \frac{256}{531441})

Stecke

x = 1

in

x^{4} (1 - x)^{8} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{1}{3}, \frac{256}{531441}), Minimum (1, 0)

Graph

Beliebte Beispiele

extreme f(x)=-xe^{-x/4}

e x t re m e f (x) = - x e^{- \frac{x}{4}}

extreme f(x)=2x^3+6x^2-18x+1,-6<= x<= 2

e x t re m e f (x) = 2 x^{3} + 6 x^{2} - 18 x + 1, - 6 \leq x \leq 2

extreme f(x)=6x+7x^{(6/7)}

e x t re m e f (x) = 6 x + 7 x^{(\frac{6}{7})}

extreme x(2^{-5x})

e x t re m e x (2^{- 5 x})

extreme f(x)=x^{2x}

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