extreme 2x^3-3x^2-12x+18

Lösung

extrempunkte

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

Maximum (- 1, 25), Minimum (2, - 2)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 1

2 x^{3} - 3 x^{2} - 12 x + 18 : 25

Maximum (- 1, 25)

Stecke

x = 2

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

Minimum (2, - 2)

Maximum (- 1, 25), Minimum (2, - 2)

e x t re m e f (x) = x^{6} - 3 x^{4}

e x t re m e f (x, y) = x^{2} + 3 x y + 4 y^{2} - 6 x + 2 y

e x t re m e f (x) = 250 + 8 x^{3} + x^{4}

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

e x t re m e f (x, y) = (x - 1)^{2} + y^{3} - 3 y^{2} - 9 y + 5