extreme f(x)=x^3-3x^2-3x-1

Lösung

extrempunkte

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

Maximum (1 - 2, 42 - 6), Minimum (1 + 2, - 6 - 42)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 2 + 1,

Absteigend

: - 2 + 1 < x < 2 + 1,

Ansteigend

: 2 + 1 < x < \infty

Stecke

x = 1 - 2

x^{3} - 3 x^{2} - 3 x - 1 : 42 - 6

Maximum (1 - 2, 42 - 6)

Stecke

x = 1 + 2

x^{3} - 3 x^{2} - 3 x - 1 : - 6 - 42

Minimum (1 + 2, - 6 - 42)

Maximum (1 - 2, 42 - 6), Minimum (1 + 2, - 6 - 42)

e x t re m e f (x) = 4 x^{2} - 8 x + 3

e x t re m e f (x, y) = x^{2} + x y + \frac{1}{2} y^{2} - 5 x + y

e x t re m e f (x, y) = ln (x^{2} + y^{2}) - x - y^{2}

e x t re m e (x^{2} + 3 x - 1)^{\frac{1}{3}}

e x t re m e f (x, y) = 5 x^{2} + 5 y^{2} + 20 x - 10 y + 40