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Beliebt Funktionen >

extreme x^4-8x^3+7x^2+6x-4

Lösung

extrempunkte

x^{4} - 8 x^{3} + 7 x^{2} + 6 x - 4

Lösung

Minimum (\frac{5 - 31}{2}, \frac{1951 - 350 31}{4} + 10331 - 579), Maximum (1, 2), Minimum (\frac{5 + 31}{2}, \frac{1951 + 350 31}{4} - 579 - 10331)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 24 x^{2} + 14 x + 6

Intervalle finden:

Absteigend

: - \infty < x < \frac{5 - 31}{2},

Ansteigend

: \frac{5 - 31}{2} < x < 1,

Absteigend

: 1 < x < \frac{5 + 31}{2},

Ansteigend

: \frac{5 + 31}{2} < x < \infty

Stecke

x = \frac{5 - 31}{2}

in

x^{4} - 8 x^{3} + 7 x^{2} + 6 x - 4 : \frac{1951 - 350 31}{4} + 10331 - 579

Minimum (\frac{5 - 31}{2}, \frac{1951 - 350 31}{4} + 10331 - 579)

Stecke

x = 1

in

x^{4} - 8 x^{3} + 7 x^{2} + 6 x - 4 : 2

Maximum (1, 2)

Stecke

x = \frac{5 + 31}{2}

in

x^{4} - 8 x^{3} + 7 x^{2} + 6 x - 4 : \frac{1951 + 350 31}{4} - 579 - 10331

Minimum (\frac{5 + 31}{2}, \frac{1951 + 350 31}{4} - 579 - 10331)

Minimum (\frac{5 - 31}{2}, \frac{1951 - 350 31}{4} + 10331 - 579), Maximum (1, 2), Minimum (\frac{5 + 31}{2}, \frac{1951 + 350 31}{4} - 579 - 10331)

Graph

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