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Beliebt Funktionen >

extreme f(x)=(x^2-25)^2

Lösung

extrempunkte

f (x) = (x^{2} - 25)^{2}

Lösung

Minimum (- 5, 0), Maximum (0, 625), Minimum (5, 0)

Schritte zur Lösung

f^{'} (x) = 4 x (x^{2} - 25)

Intervalle finden:

Absteigend

: - \infty < x < - 5,

Ansteigend

: - 5 < x < 0,

Absteigend

: 0 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = - 5

in

(x^{2} - 25)^{2} : 0

Minimum (- 5, 0)

Stecke

x = 0

in

(x^{2} - 25)^{2} : 625

Maximum (0, 625)

Stecke

x = 5

in

(x^{2} - 25)^{2} : 0

Minimum (5, 0)

Minimum (- 5, 0), Maximum (0, 625), Minimum (5, 0)

Graph

Beliebte Beispiele

extreme (x^2+12)(144-x^2)

e x t re m e (x^{2} + 12) (144 - x^{2})

extreme f(x)=(10x^3)/3-(11x^2)/2+x+2

e x t re m e f (x) = \frac{10 x ^{3}}{3} - \frac{11 x ^{2}}{2} + x + 2

extreme f(x)=x^2+3,-1<= x<= 4

e x t re m e f (x) = x^{2} + 3, - 1 \leq x \leq 4

extreme f(x,y)=5x+5y

e x t re m e f (x, y) = 5 x + 5 y

extreme f(x,y)=x^2-2y^2+8x-3y+1

e x t re m e f (x, y) = x^{2} - 2 y^{2} + 8 x - 3 y + 1