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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (- 1, 0), Minimum (- \frac{1}{3}, - \frac{4}{27}), Maximum (0, 0), Minimum (\frac{1}{3}, - \frac{4}{27}), Maximum (1, 0)

Schritte zur Lösung

f^{'} (x) = - 6 x^{5} + 8 x^{3} - 2 x

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < - \frac{1}{3},

Ansteigend

: - \frac{1}{3} < x < 0,

Absteigend

: 0 < x < \frac{1}{3},

Ansteigend

: \frac{1}{3} < x < 1,

Absteigend

: 1 < x < \infty

Stecke

x = - 1

in

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

Maximum (- 1, 0)

Stecke

x = - \frac{1}{3}

in

- x^{2} (x + 1)^{2} (x - 1)^{2} : - \frac{4}{27}

Minimum (- \frac{1}{3}, - \frac{4}{27})

Stecke

x = 0

in

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

Maximum (0, 0)

Stecke

x = \frac{1}{3}

in

- x^{2} (x + 1)^{2} (x - 1)^{2} : - \frac{4}{27}

Minimum (\frac{1}{3}, - \frac{4}{27})

Stecke

x = 1

in

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

Maximum (1, 0)

Maximum (- 1, 0), Minimum (- \frac{1}{3}, - \frac{4}{27}), Maximum (0, 0), Minimum (\frac{1}{3}, - \frac{4}{27}), Maximum (1, 0)

Graph

Beliebte Beispiele

solvefor V,V=pir2h

so l v e f or V, V = π r 2 h

extreme f(x)=-1000x^3-1000x^2+8000x+1000

e x t re m e f (x) = - 1000 x^{3} - 1000 x^{2} + 8000 x + 1000

extreme 1/x+ln(x)

e x t re m e \frac{1}{x} + ln (x)

extreme f(x)=x^3-3xy+y^3

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

extreme f(x,y)=y^2e^{-x+ln(y)}

e x t re m e f (x, y) = y^{2} e^{- x + l n (y)}