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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (0, 0), Maximum (\frac{3}{2}, \frac{3 3}{4}), Minimum (2, 0)

Schritte zur Lösung

f^{'} (x) = \frac{- 2 x ^{2} + 3 x}{2 x - x ^{2}}

Intervalle finden:

Ansteigend

: 0 < x < \frac{3}{2},

Absteigend

: \frac{3}{2} < x < 2

Stecke

x = 0

in

x 2 x - x^{2} : 0

Minimum (0, 0)

Stecke

x = \frac{3}{2}

in

x 2 x - x^{2} : \frac{3 3}{4}

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

Stecke

x = 2

in

x 2 x - x^{2} : 0

Minimum (2, 0)

Minimum (0, 0), Maximum (\frac{3}{2}, \frac{3 3}{4}), Minimum (2, 0)

Graph

Beliebte Beispiele

extreme f(x)=(2-4x)/(3+x)

e x t re m e f (x) = \frac{2 - 4 x}{3 + x}

extreme f(x,y)= 23/2 y^4-46xy+23x^2

e x t re m e f (x, y) = \frac{23}{2} y^{4} - 46 x y + 23 x^{2}

extreme-8x^{5/3}+\sqrt[3]{x}

e x t re m e - 8 x^{\frac{5}{3}} + 3 x

extreme f(x,y)=2x^3+6xy+3y^2

e x t re m e f (x, y) = 2 x^{3} + 6 x y + 3 y^{2}

extreme f(x,y)=16x\sqrt[3]{y}-2x^2-4x-16y+2

e x t re m e f (x, y) = 16 x 3 y - 2 x^{2} - 4 x - 16 y + 2