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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (\frac{1}{3}, \frac{35}{27}), Minimum (1, 1)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} - 8 x + 2

Intervalle finden:

Ansteigend

: - \infty < x < \frac{1}{3},

Absteigend

: \frac{1}{3} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = \frac{1}{3}

in

2 x^{3} - 4 x^{2} + 2 x + 1 : \frac{35}{27}

Maximum (\frac{1}{3}, \frac{35}{27})

Stecke

x = 1

in

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

Minimum (1, 1)

Maximum (\frac{1}{3}, \frac{35}{27}), Minimum (1, 1)

Graph

Beliebte Beispiele

extreme 4-3x-x^3

e x t re m e 4 - 3 x - x^{3}

extreme f(x)=4-x^3

e x t re m e f (x) = 4 - x^{3}

extreme-2x^2+4x+8

e x t re m e - 2 x^{2} + 4 x + 8

extreme f(xy)=x^2+2y^2-xy+14y

e x t re m e f (x y) = x^{2} + 2 y^{2} - x y + 14 y

extreme (x+1)/(x^2-7x-8)

e x t re m e \frac{x + 1}{x ^{2} - 7 x - 8}