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Beliebt Funktionen >

extreme f(x)=x^2(x-5)^2

Lösung

extrempunkte

f (x) = x^{2} (x - 5)^{2}

Lösung

Minimum (0, 0), Maximum (\frac{5}{2}, \frac{625}{16}), Minimum (5, 0)

Schritte zur Lösung

f^{'} (x) = 2 x (x - 5) (2 x - 5)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{5}{2},

Absteigend

: \frac{5}{2} < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = 0

in

x^{2} (x - 5)^{2} : 0

Minimum (0, 0)

Stecke

x = \frac{5}{2}

in

x^{2} (x - 5)^{2} : \frac{625}{16}

Maximum (\frac{5}{2}, \frac{625}{16})

Stecke

x = 5

in

x^{2} (x - 5)^{2} : 0

Minimum (5, 0)

Minimum (0, 0), Maximum (\frac{5}{2}, \frac{625}{16}), Minimum (5, 0)

Graph

Beliebte Beispiele

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

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

extreme f(x)=x+yx^3

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

extreme f(x)=5+54x-2x^3,0<= x<= 4

e x t re m e f (x) = 5 + 54 x - 2 x^{3}, 0 \leq x \leq 4

extreme f(x)= 1/(x+y)

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

extreme f(x)=sin(x)+cos(x),(0,2pi)

e x t re m e f (x) = sin (x) + cos (x), (0, 2 π)