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Beliebt Funktionen >

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

Lösung

extrempunkte

f (x) = (x - 1)^{2} (x + 3)^{2}

Lösung

Minimum (- 3, 0), Maximum (- 1, 16), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = 4 (x - 1) (x + 3) (x + 1)

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < - 1,

Absteigend

: - 1 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 3

in

(x - 1)^{2} (x + 3)^{2} : 0

Minimum (- 3, 0)

Stecke

x = - 1

in

(x - 1)^{2} (x + 3)^{2} : 16

Maximum (- 1, 16)

Stecke

x = 1

in

(x - 1)^{2} (x + 3)^{2} : 0

Minimum (1, 0)

Minimum (- 3, 0), Maximum (- 1, 16), Minimum (1, 0)

Graph

Beliebte Beispiele

extreme U(a,b)=aa+bb

e x t re m e U (a, b) = aa + bb

extreme f(x)= 1/3 x^3-7x^2+24x+6

e x t re m e f (x) = \frac{1}{3} x^{3} - 7 x^{2} + 24 x + 6

extreme f(x)=((4860)/x)+17x+752774

e x t re m e f (x) = (\frac{4860}{x}) + 17 x + 752774

extreme f(x)=xe^{-x^2-y^2}

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

extreme f(x)=xsqrt(600-x)

e x t re m e f (x) = x 600 - x