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Beliebt Funktionen >

extreme f(x)=18x+3x^2-4x^3

Lösung

extrempunkte

f (x) = 18 x + 3 x^{2} - 4 x^{3}

Lösung

Minimum (- 1, - 11), Maximum (\frac{3}{2}, \frac{81}{4})

Schritte zur Lösung

f^{'} (x) = 18 + 6 x - 12 x^{2}

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < \frac{3}{2},

Absteigend

: \frac{3}{2} < x < \infty

Stecke

x = - 1

in

18 x + 3 x^{2} - 4 x^{3} : - 11

Minimum (- 1, - 11)

Stecke

x = \frac{3}{2}

in

18 x + 3 x^{2} - 4 x^{3} : \frac{81}{4}

Maximum (\frac{3}{2}, \frac{81}{4})

Minimum (- 1, - 11), Maximum (\frac{3}{2}, \frac{81}{4})

Graph

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