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Beliebt Funktionen >

extreme f(x)=x^4+x^3-3x^2+1

Lösung

extrempunkte

f (x) = x^{4} + x^{3} - 3 x^{2} + 1

Lösung

Minimum (\frac{- 3 - 105}{8}, - \frac{3 ( 537 + 35 105 )}{512} + 1), Maximum (0, 1), Minimum (\frac{- 3 + 105}{8}, \frac{3 ( 35 105 - 537 )}{512} + 1)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} + 3 x^{2} - 6 x

Intervalle finden:

Absteigend

: - \infty < x < \frac{- 3 - 105}{8},

Ansteigend

: \frac{- 3 - 105}{8} < x < 0,

Absteigend

: 0 < x < \frac{105 - 3}{8},

Ansteigend

: \frac{105 - 3}{8} < x < \infty

Stecke

x = \frac{- 3 - 105}{8}

in

x^{4} + x^{3} - 3 x^{2} + 1 : - \frac{3 ( 537 + 35 105 )}{512} + 1

Minimum (\frac{- 3 - 105}{8}, - \frac{3 ( 537 + 35 105 )}{512} + 1)

Stecke

x = 0

in

x^{4} + x^{3} - 3 x^{2} + 1 : 1

Maximum (0, 1)

Stecke

x = \frac{- 3 + 105}{8}

in

x^{4} + x^{3} - 3 x^{2} + 1 : \frac{3 ( 35 105 - 537 )}{512} + 1

Minimum (\frac{- 3 + 105}{8}, \frac{3 ( 35 105 - 537 )}{512} + 1)

Minimum (\frac{- 3 - 105}{8}, - \frac{3 ( 537 + 35 105 )}{512} + 1), Maximum (0, 1), Minimum (\frac{- 3 + 105}{8}, \frac{3 ( 35 105 - 537 )}{512} + 1)

Graph

Beliebte Beispiele

e x t re m e f (x) = 9

extreme f(x,y)=(e^{xy})

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

extreme f(x)=ln(x^3-1)

e x t re m e f (x) = ln (x^{3} - 1)

extreme f(x)=2x^2+3y^2-4x-5

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extreme f(x)=-8+4ln(x)

e x t re m e f (x) = - 8 + 4 ln (x)