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Beliebt Funktionen >

extreme f(x)=4x^3-45x^2+150x

Lösung

extrempunkte

f (x) = 4 x^{3} - 45 x^{2} + 150 x

Lösung

Maximum (\frac{5}{2}, \frac{625}{4}), Minimum (5, 125)

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 90 x + 150

Intervalle finden:

Ansteigend

: - \infty < x < \frac{5}{2},

Absteigend

: \frac{5}{2} < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = \frac{5}{2}

in

4 x^{3} - 45 x^{2} + 150 x : \frac{625}{4}

Maximum (\frac{5}{2}, \frac{625}{4})

Stecke

x = 5

in

4 x^{3} - 45 x^{2} + 150 x : 125

Minimum (5, 125)

Maximum (\frac{5}{2}, \frac{625}{4}), Minimum (5, 125)

Graph

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