extreme f(x)=-2x^3+6x^2-5

Lösung

extrempunkte

f (x) = - 2 x^{3} + 6 x^{2} - 5

Minimum (0, - 5), Maximum (2, 3)

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 12 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 0

- 2 x^{3} + 6 x^{2} - 5 : - 5

Minimum (0, - 5)

Stecke

x = 2

- 2 x^{3} + 6 x^{2} - 5 : 3

Maximum (2, 3)

Minimum (0, - 5), Maximum (2, 3)

e x t re m e x^{4} - 8 x^{3} + 16 x^{2}

e x t re m e f (x) = x^{3} + y^{3} - 3 x^{2} - 9 y^{2} - 9 x

e x t re m e f (x, y) = 2 x^{2} - 8 x + y^{2} - 8 y + 6

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

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