extreme f(x)=-2x^3+12x^2+18

Lösung

extrempunkte

f (x) = - 2 x^{3} + 12 x^{2} + 18

Minimum (0, 18), Maximum (4, 82)

Schritte zur Lösung

f^{'} (x) = - 6 x^{2} + 24 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = 0

- 2 x^{3} + 12 x^{2} + 18 : 18

Minimum (0, 18)

Stecke

x = 4

- 2 x^{3} + 12 x^{2} + 18 : 82

Maximum (4, 82)

Minimum (0, 18), Maximum (4, 82)

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

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

e x t re m e f (x, y) = 2 x y - 5 x^{2} - 2 y^{2} + 18 y - 8

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

e x t re m e f (x) = \frac{1}{4} x^{4} + \frac{4}{3} x^{3} + 2 x^{2}