extreme-x^3+27x-55

Lösung

extrempunkte

- x^{3} + 27 x - 55

Minimum (- 3, - 109), Maximum (3, - 1)

Schritte zur Lösung

f^{'} (x) = - 3 x^{2} + 27

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 3

- x^{3} + 27 x - 55 : - 109

Minimum (- 3, - 109)

Stecke

x = 3

- x^{3} + 27 x - 55 : - 1

Maximum (3, - 1)

Minimum (- 3, - 109), Maximum (3, - 1)

e x t re m e f (x, y, λ) = 9 - x^{2} - y^{2} + λ (4 - x - y)

e x t re m e f (x, y) = 7 x^{2} + 6 x y + 5 y^{2} + 4 x y^{2} + 7 x^{2} y

e x t re m e f (x) = 8 x - 2 x^{2} + 12 x y - 12 y^{2} + y

e x t re m e f (x) = 2 x^{2} + 3 x - 5, - 4 \leq x \leq 4

e x t re m e f (x, y) = x^{3} + y^{3} - 3 x - 12 y + 13 e