extreme f(x)=2x^3+30x^2+144x-1

Lösung

extrempunkte

f (x) = 2 x^{3} + 30 x^{2} + 144 x - 1

Maximum (- 6, - 217), Minimum (- 4, - 225)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} + 60 x + 144

Intervalle finden:

Ansteigend

: - \infty < x < - 6,

Absteigend

: - 6 < x < - 4,

Ansteigend

: - 4 < x < \infty

Stecke

x = - 6

2 x^{3} + 30 x^{2} + 144 x - 1 : - 217

Maximum (- 6, - 217)

Stecke

x = - 4

2 x^{3} + 30 x^{2} + 144 x - 1 : - 225

Minimum (- 4, - 225)

Maximum (- 6, - 217), Minimum (- 4, - 225)

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