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Beliebt Funktionen >

extreme y=(2x^2-1)^2

Lösung

extrempunkte

y = (2 x^{2} - 1)^{2}

Lösung

Minimum (- \frac{1}{2}, 0), Maximum (0, 1), Minimum (\frac{1}{2}, 0)

Schritte zur Lösung

f^{'} (x) = 8 x (2 x^{2} - 1)

Intervalle finden:

Absteigend

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

Ansteigend

: - \frac{1}{2} < x < 0,

Absteigend

: 0 < x < \frac{1}{2},

Ansteigend

: \frac{1}{2} < x < \infty

Stecke

x = - \frac{1}{2}

in

(2 x^{2} - 1)^{2} : 0

Minimum (- \frac{1}{2}, 0)

Stecke

x = 0

in

(2 x^{2} - 1)^{2} : 1

Maximum (0, 1)

Stecke

x = \frac{1}{2}

in

(2 x^{2} - 1)^{2} : 0

Minimum (\frac{1}{2}, 0)

Minimum (- \frac{1}{2}, 0), Maximum (0, 1), Minimum (\frac{1}{2}, 0)

Graph

Beliebte Beispiele

extreme f(x)= 6/(-4x+2)

e x t re m e f (x) = \frac{6}{- 4 x + 2}

extreme f(y)=x^{y+1}

e x t re m e f (y) = x^{y + 1}

extreme f(x)=x^2log_{8}(x)

e x t re m e f (x) = x^{2} lo g_{8} (x)

extreme x+(192)/x

e x t re m e x + \frac{192}{x}

extreme f(x)=-(x^2)/(10)+2x+3

e x t re m e f (x) = - \frac{x ^{2}}{10} + 2 x + 3