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Beliebt Funktionen >

extreme f(x)=x^5-4x^3+4x-1

Lösung

extrempunkte

f (x) = x^{5} - 4 x^{3} + 4 x - 1

Lösung

Maximum (- 2, - 1), Minimum (- \frac{2}{5}, - (\frac{2}{5})^{\frac{5}{2}} + 4 (\frac{2}{5})^{\frac{3}{2}} - 4 \frac{2}{5} - 1), Maximum (\frac{2}{5}, (\frac{2}{5})^{\frac{5}{2}} - 4 (\frac{2}{5})^{\frac{3}{2}} + 4 \frac{2}{5} - 1), Minimum (2, - 1)

Schritte zur Lösung

f^{'} (x) = 5 x^{4} - 12 x^{2} + 4

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < - \frac{2}{5},

Ansteigend

: - \frac{2}{5} < x < \frac{2}{5},

Absteigend

: \frac{2}{5} < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 2

in

x^{5} - 4 x^{3} + 4 x - 1 : - 1

Maximum (- 2, - 1)

Stecke

x = - \frac{2}{5}

in

x^{5} - 4 x^{3} + 4 x - 1 : - (\frac{2}{5})^{\frac{5}{2}} + 4 (\frac{2}{5})^{\frac{3}{2}} - 4 \frac{2}{5} - 1

Minimum (- \frac{2}{5}, - (\frac{2}{5})^{\frac{5}{2}} + 4 (\frac{2}{5})^{\frac{3}{2}} - 4 \frac{2}{5} - 1)

Stecke

x = \frac{2}{5}

in

x^{5} - 4 x^{3} + 4 x - 1 : (\frac{2}{5})^{\frac{5}{2}} - 4 (\frac{2}{5})^{\frac{3}{2}} + 4 \frac{2}{5} - 1

Maximum (\frac{2}{5}, (\frac{2}{5})^{\frac{5}{2}} - 4 (\frac{2}{5})^{\frac{3}{2}} + 4 \frac{2}{5} - 1)

Stecke

x = 2

in

x^{5} - 4 x^{3} + 4 x - 1 : - 1

Minimum (2, - 1)

Maximum (- 2, - 1), Minimum (- \frac{2}{5}, - (\frac{2}{5})^{\frac{5}{2}} + 4 (\frac{2}{5})^{\frac{3}{2}} - 4 \frac{2}{5} - 1), Maximum (\frac{2}{5}, (\frac{2}{5})^{\frac{5}{2}} - 4 (\frac{2}{5})^{\frac{3}{2}} + 4 \frac{2}{5} - 1), Minimum (2, - 1)

Graph

Beliebte Beispiele

interzeption xe^x

in t erce pt s x e^{x}

bereich f(x)=sqrt(x+7)

r an g e f (x) = x + 7

invers f(x)=6-x^2

in v erse f (x) = 6 - x^{2}

entfernung (0,0),(-5,-5)

d i s t an ce (0, 0), (- 5, - 5)

invers (83.66)/(88.29)

in v erse \frac{83.66}{88.29}