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Beliebt Funktionen >

extreme f(x)=12x^4-4x^2+6

Lösung

extrempunkte

f (x) = 12 x^{4} - 4 x^{2} + 6

Lösung

Minimum (- \frac{1}{6}, \frac{17}{3}), Maximum (0, 6), Minimum (\frac{1}{6}, \frac{17}{3})

Schritte zur Lösung

f^{'} (x) = 48 x^{3} - 8 x

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{6},

Ansteigend

: - \frac{1}{6} < x < 0,

Absteigend

: 0 < x < \frac{1}{6},

Ansteigend

: \frac{1}{6} < x < \infty

Stecke

x = - \frac{1}{6}

in

12 x^{4} - 4 x^{2} + 6 : \frac{17}{3}

Minimum (- \frac{1}{6}, \frac{17}{3})

Stecke

x = 0

in

12 x^{4} - 4 x^{2} + 6 : 6

Maximum (0, 6)

Stecke

x = \frac{1}{6}

in

12 x^{4} - 4 x^{2} + 6 : \frac{17}{3}

Minimum (\frac{1}{6}, \frac{17}{3})

Minimum (- \frac{1}{6}, \frac{17}{3}), Maximum (0, 6), Minimum (\frac{1}{6}, \frac{17}{3})

Graph

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