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Beliebt Funktionen >

extreme f(x)=x^2sqrt(4-x)

Lösung

extrempunkte

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

Lösung

Minimum (0, 0), Maximum (\frac{16}{5}, \frac{512}{25 5}), Minimum (4, 0)

Schritte zur Lösung

f^{'} (x) = \frac{x ( - 5 x + 16 )}{2 4 - x}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{16}{5},

Absteigend

: \frac{16}{5} < x < 4

Stecke

x = 0

in

x^{2} 4 - x : 0

Minimum (0, 0)

Stecke

x = \frac{16}{5}

in

x^{2} 4 - x : \frac{512}{25 5}

Maximum (\frac{16}{5}, \frac{512}{25 5})

Stecke

x = 4

in

x^{2} 4 - x : 0

Minimum (4, 0)

Minimum (0, 0), Maximum (\frac{16}{5}, \frac{512}{25 5}), Minimum (4, 0)

Graph

Beliebte Beispiele

extreme f(x)=3x^3y-2xy^2

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

extreme f(x,y)=2x^3+4y^3+3x^2-12x-192y+5

e x t re m e f (x, y) = 2 x^{3} + 4 y^{3} + 3 x^{2} - 12 x - 192 y + 5

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

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

extreme f(x)=215x-3x^2-650-5x

e x t re m e f (x) = 215 x - 3 x^{2} - 650 - 5 x

extreme f(x)=8x^2+48x

e x t re m e f (x) = 8 x^{2} + 48 x