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Beliebt Funktionen >

extreme f(x)=1+80x^3+5x^4-2x^5

Lösung

extrempunkte

f (x) = 1 + 80 x^{3} + 5 x^{4} - 2 x^{5}

Lösung

Minimum (- 4, - 1791), Sattel (0, 1), Maximum (6, 8209)

Schritte zur Lösung

f^{'} (x) = - 10 x^{4} + 20 x^{3} + 240 x^{2}

Intervalle finden:

Absteigend

: - \infty < x < - 4,

Ansteigend

: - 4 < x < 0,

Ansteigend

: 0 < x < 6,

Absteigend

: 6 < x < \infty

Stecke

x = - 4

in

1 + 80 x^{3} + 5 x^{4} - 2 x^{5} : - 1791

Minimum (- 4, - 1791)

Stecke

x = 0

in

1 + 80 x^{3} + 5 x^{4} - 2 x^{5} : 1

Sattel (0, 1)

Stecke

x = 6

in

1 + 80 x^{3} + 5 x^{4} - 2 x^{5} : 8209

Maximum (6, 8209)

Minimum (- 4, - 1791), Sattel (0, 1), Maximum (6, 8209)

Graph

Beliebte Beispiele

extreme f(x)=18xy-x^3-9y^2

e x t re m e f (x) = 18 x y - x^{3} - 9 y^{2}

extreme f(x)=15x^4-4x^3,-2<= x<= 2

e x t re m e f (x) = 15 x^{4} - 4 x^{3}, - 2 \leq x \leq 2

extreme y=2x^3-24x^2+90x+8

e x t re m e y = 2 x^{3} - 24 x^{2} + 90 x + 8

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

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

extreme f(x)=4x^3-24x^2+36x

e x t re m e f (x) = 4 x^{3} - 24 x^{2} + 36 x