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Beliebt Funktionen >

extreme f(x)=30x^4-13x^3-54x^2-1

Lösung

extrempunkte

f (x) = 30 x^{4} - 13 x^{3} - 54 x^{2} - 1

Lösung

Minimum (- \frac{4}{5}, - \frac{2077}{125}), Maximum (0, - 1), Minimum (\frac{9}{8}, - \frac{81509}{2048})

Schritte zur Lösung

f^{'} (x) = 120 x^{3} - 39 x^{2} - 108 x

Intervalle finden:

Absteigend

: - \infty < x < - \frac{4}{5},

Ansteigend

: - \frac{4}{5} < x < 0,

Absteigend

: 0 < x < \frac{9}{8},

Ansteigend

: \frac{9}{8} < x < \infty

Stecke

x = - \frac{4}{5}

in

30 x^{4} - 13 x^{3} - 54 x^{2} - 1 : - \frac{2077}{125}

Minimum (- \frac{4}{5}, - \frac{2077}{125})

Stecke

x = 0

in

30 x^{4} - 13 x^{3} - 54 x^{2} - 1 : - 1

Maximum (0, - 1)

Stecke

x = \frac{9}{8}

in

30 x^{4} - 13 x^{3} - 54 x^{2} - 1 : - \frac{81509}{2048}

Minimum (\frac{9}{8}, - \frac{81509}{2048})

Minimum (- \frac{4}{5}, - \frac{2077}{125}), Maximum (0, - 1), Minimum (\frac{9}{8}, - \frac{81509}{2048})

Graph

Beliebte Beispiele

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

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

extreme f(x)=8-x,-1<= x<= 3

e x t re m e f (x) = 8 - x, - 1 \leq x \leq 3

extreme P(x,y)=x^2+5xy-4y^2

e x t re m e P (x, y) = x^{2} + 5 x y - 4 y^{2}

extreme f(x)=cos(3x),-1/6 pi<x< 1/2 pi

e x t re m e f (x) = cos (3 x), - \frac{1}{6} π < x < \frac{1}{2} π

extreme f(x)=8x^3

e x t re m e f (x) = 8 x^{3}