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Beliebt Funktionen >

extreme f(x)=x^4(x+2)^2

Lösung

extrempunkte

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

Lösung

Minimum (- 2, 0), Maximum (- \frac{4}{3}, \frac{1024}{729}), Minimum (0, 0)

Schritte zur Lösung

f^{'} (x) = 2 x^{3} (x + 2) (3 x + 4)

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < - \frac{4}{3},

Absteigend

: - \frac{4}{3} < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - 2

in

x^{4} (x + 2)^{2} : 0

Minimum (- 2, 0)

Stecke

x = - \frac{4}{3}

in

x^{4} (x + 2)^{2} : \frac{1024}{729}

Maximum (- \frac{4}{3}, \frac{1024}{729})

Stecke

x = 0

in

x^{4} (x + 2)^{2} : 0

Minimum (0, 0)

Minimum (- 2, 0), Maximum (- \frac{4}{3}, \frac{1024}{729}), Minimum (0, 0)

Graph

Beliebte Beispiele

extreme f(x)=(x+3)/(x^2-4x-21)

e x t re m e f (x) = \frac{x + 3}{x ^{2} - 4 x - 21}

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

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

extreme f(x)=x^{(2/3)}

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

extreme f(x)=((x+4))/(x^2-3x-28)

e x t re m e f (x) = \frac{( x + 4 )}{x ^{2} - 3 x - 28}

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

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