extreme f(x)=2x^3+3x^2-36x+4

Lösung

extrempunkte

f (x) = 2 x^{3} + 3 x^{2} - 36 x + 4

Maximum (- 3, 85), Minimum (2, - 40)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} + 6 x - 36

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - 3

2 x^{3} + 3 x^{2} - 36 x + 4 : 85

Maximum (- 3, 85)

Stecke

x = 2

2 x^{3} + 3 x^{2} - 36 x + 4 : - 40

Minimum (2, - 40)

Maximum (- 3, 85), Minimum (2, - 40)

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

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

e x t re m e f (x) = 8 x - x^{4}, - 2 \leq x \leq 1

e x t re m e f (x, y) = 2 x^{2} + 4 x y^{2} - 2 x y - 10 x - 2 y + 2

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