extreme x^3-3x^2+1

Lösung

extrempunkte

x^{3} - 3 x^{2} + 1

Maximum (0, 1), Minimum (2, - 3)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 6 x

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = 0

x^{3} - 3 x^{2} + 1 : 1

Maximum (0, 1)

Stecke

x = 2

x^{3} - 3 x^{2} + 1 : - 3

Minimum (2, - 3)

Maximum (0, 1), Minimum (2, - 3)

e x t re m e f (x) = \frac{8}{135} x^{3} - \frac{1}{20} x^{2} - \frac{7}{16} x

e x t re m e f (x) = - x^{2} (x + 1)^{2} (x - 1)^{2}

so l v e f or V, V = π r 2 h

e x t re m e f (x) = - 1000 x^{3} - 1000 x^{2} + 8000 x + 1000

e x t re m e \frac{1}{x} + ln (x)