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Beliebt Funktionen >

extreme (x+3)^2(x^3-x^2)

Lösung

extrempunkte

(x + 3)^{2} (x^{3} - x^{2})

Lösung

Maximum (- 3, 0), Minimum (\frac{- 5 - 145}{10}, - \frac{950 + 58 145}{125}), Maximum (0, 0), Minimum (\frac{- 5 + 145}{10}, \frac{58 145 - 950}{125})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < \frac{- 5 - 145}{10},

Ansteigend

: \frac{- 5 - 145}{10} < x < 0,

Absteigend

: 0 < x < \frac{145 - 5}{10},

Ansteigend

: \frac{145 - 5}{10} < x < \infty

Stecke

x = - 3

in

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

Maximum (- 3, 0)

Stecke

x = \frac{- 5 - 145}{10}

in

(x + 3)^{2} (x^{3} - x^{2}) : - \frac{950 + 58 145}{125}

Minimum (\frac{- 5 - 145}{10}, - \frac{950 + 58 145}{125})

Stecke

x = 0

in

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

Maximum (0, 0)

Stecke

x = \frac{- 5 + 145}{10}

in

(x + 3)^{2} (x^{3} - x^{2}) : \frac{58 145 - 950}{125}

Minimum (\frac{- 5 + 145}{10}, \frac{58 145 - 950}{125})

Maximum (- 3, 0), Minimum (\frac{- 5 - 145}{10}, - \frac{950 + 58 145}{125}), Maximum (0, 0), Minimum (\frac{- 5 + 145}{10}, \frac{58 145 - 950}{125})

Graph

Beliebte Beispiele

extreme f(x)=(x+2)^3-5

e x t re m e f (x) = (x + 2)^{3} - 5

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

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

extreme f(x)=6x^{2/3}

e x t re m e f (x) = 6 x^{\frac{2}{3}}

extreme 2x^3+3x^2-72x

e x t re m e 2 x^{3} + 3 x^{2} - 72 x

extreme f(x,y)=4x^2-xy+9y^2

e x t re m e f (x, y) = 4 x^{2} - x y + 9 y^{2}