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Beliebt Funktionen >

extreme f(x)=x^2*(2-x)^2

Lösung

extrempunkte

f (x) = x^{2} \cdot (2 - x)^{2}

Lösung

Minimum (0, 0), Maximum (1, 1), Minimum (2, 0)

Schritte zur Lösung

f^{'} (x) = 4 x (x - 2) (x - 1)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 1,

Absteigend

: 1 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = 0

in

x^{2} \cdot (2 - x)^{2} : 0

Minimum (0, 0)

Stecke

x = 1

in

x^{2} \cdot (2 - x)^{2} : 1

Maximum (1, 1)

Stecke

x = 2

in

x^{2} \cdot (2 - x)^{2} : 0

Minimum (2, 0)

Minimum (0, 0), Maximum (1, 1), Minimum (2, 0)

Graph

Beliebte Beispiele

extreme f(x,y)=4x^2-8x+5y^2+6

e x t re m e f (x, y) = 4 x^{2} - 8 x + 5 y^{2} + 6

extreme-(x^2-y^2)e^{-x^2-y^2}

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

extreme 6sqrt(3cos(x)+6sin^2(x))

e x t re m e 6 3 cos (x) + 6 sin^{2} (x)

extreme ((4x-12))/((x-2)^2)

e x t re m e \frac{( 4 x - 12 )}{( x - 2 ) ^{2}}

extreme f(x,y)=x+3y

e x t re m e f (x, y) = x + 3 y