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Beliebt Funktionen >

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

Lösung

extrempunkte

f (x) = (x + 1) ln^{2} (x + 1)

Lösung

Maximum (\frac{1}{e ^{2}} - 1, \frac{4}{e ^{2}}), Minimum (0, 0)

Schritte zur Lösung

f^{'} (x) = ln (x + 1) (ln (x + 1) + 2)

Intervalle finden:

Ansteigend

: - 1 < x < \frac{1}{e ^{2}} - 1,

Absteigend

: \frac{1}{e ^{2}} - 1 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = \frac{1}{e ^{2}} - 1

in

(x + 1) ln^{2} (x + 1) : \frac{4}{e ^{2}}

Maximum (\frac{1}{e ^{2}} - 1, \frac{4}{e ^{2}})

Stecke

x = 0

in

(x + 1) ln^{2} (x + 1) : 0

Minimum (0, 0)

Maximum (\frac{1}{e ^{2}} - 1, \frac{4}{e ^{2}}), Minimum (0, 0)

Graph

Beliebte Beispiele

extreme f(x)=x^2-6x-1,0<= x<= 3

e x t re m e f (x) = x^{2} - 6 x - 1, 0 \leq x \leq 3

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

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extreme g(x)=x^3-x^2-8x-5

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extreme 2x^3-x^2-4x+4

e x t re m e 2 x^{3} - x^{2} - 4 x + 4