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Beliebt Funktionen >

extreme f(x)=(x-5)(x-3)(x+1)^2

Lösung

extrempunkte

f (x) = (x - 5) (x - 3) (x + 1)^{2}

Lösung

Minimum (- 1, 0), Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15), Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Schritte zur Lösung

f^{'} (x) = 2 (x + 1) (2 x^{2} - 11 x + 11)

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < \frac{11 - 33}{4},

Absteigend

: \frac{11 - 33}{4} < x < \frac{11 + 33}{4},

Ansteigend

: \frac{11 + 33}{4} < x < \infty

Stecke

x = - 1

in

(x - 5) (x - 3) (x + 1)^{2} : 0

Minimum (- 1, 0)

Stecke

x = \frac{11 - 33}{4}

in

(x - 5) (x - 3) (x + 1)^{2} : \frac{165 33 - 363}{32} + 15

Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15)

Stecke

x = \frac{11 + 33}{4}

in

(x - 5) (x - 3) (x + 1)^{2} : \frac{- 363 - 165 33}{32} + 15

Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Minimum (- 1, 0), Maximum (\frac{11 - 33}{4}, \frac{165 33 - 363}{32} + 15), Minimum (\frac{11 + 33}{4}, \frac{- 363 - 165 33}{32} + 15)

Graph

Beliebte Beispiele

extreme y=x^3-3x^2-9x+1

e x t re m e y = x^{3} - 3 x^{2} - 9 x + 1

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e x t re m e f (x, y) = 3 x^{2} + y^{2}

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

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extreme 3x^2+y^2-xy-11x

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