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Beliebt Funktionen >

extreme 16(x-1)^4-4(x-1)^2+1

Lösung

extrempunkte

16 (x - 1)^{4} - 4 (x - 1)^{2} + 1

Lösung

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

Schritte zur Lösung

f^{'} (x) = 64 x^{3} - 192 x^{2} + 184 x - 56

Intervalle finden:

Absteigend

: - \infty < x < \frac{4 - 2}{4},

Ansteigend

: \frac{4 - 2}{4} < x < 1,

Absteigend

: 1 < x < \frac{4 + 2}{4},

Ansteigend

: \frac{4 + 2}{4} < x < \infty

Stecke

x = \frac{4 - 2}{4}

in

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

Minimum (\frac{4 - 2}{4}, \frac{3}{4})

Stecke

x = 1

in

16 (x - 1)^{4} - 4 (x - 1)^{2} + 1 : 1

Maximum (1, 1)

Stecke

x = \frac{4 + 2}{4}

in

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

Minimum (\frac{4 + 2}{4}, \frac{3}{4})

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

Graph

Beliebte Beispiele

extreme f(x,y)=x^2+3xy+y-1

e x t re m e f (x, y) = x^{2} + 3 x y + y - 1

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

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

extreme f(x,y)=6x-4y-x^2-2y^2

e x t re m e f (x, y) = 6 x - 4 y - x^{2} - 2 y^{2}

extreme f(x,y)=10x^2y-5x^2-4y^2-x^4-2y^4

e x t re m e f (x, y) = 10 x^{2} y - 5 x^{2} - 4 y^{2} - x^{4} - 2 y^{4}

extreme f(x,y)=xy^2+2xy+3x^3-3x

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