extreme x^3-9x^2+24x-12

Lösung

extrempunkte

x^{3} - 9 x^{2} + 24 x - 12

Maximum (2, 8), Minimum (4, 4)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 18 x + 24

Intervalle finden:

Ansteigend

: - \infty < x < 2,

Absteigend

: 2 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 2

x^{3} - 9 x^{2} + 24 x - 12 : 8

Maximum (2, 8)

Stecke

x = 4

x^{3} - 9 x^{2} + 24 x - 12 : 4

Minimum (4, 4)

Maximum (2, 8), Minimum (4, 4)

e x t re m e 9 - x^{2}, - 3 \leq x \leq 2

e x t re m e f (x) = \frac{x ^{6}}{10} - \frac{2 x ^{5}}{3}

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

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

e x t re m e f (x, y) = x^{2} + x y + y^{2} - 31 y + 320