extreme f(x)=2x^3-6x^2-48x+9

Lösung

extrempunkte

f (x) = 2 x^{3} - 6 x^{2} - 48 x + 9

Maximum (- 2, 65), Minimum (4, - 151)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} - 12 x - 48

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = - 2

2 x^{3} - 6 x^{2} - 48 x + 9 : 65

Maximum (- 2, 65)

Stecke

x = 4

2 x^{3} - 6 x^{2} - 48 x + 9 : - 151

Minimum (4, - 151)

Maximum (- 2, 65), Minimum (4, - 151)

e x t re m e y = x^{2} - 3 x + 2

e x t re m e f (x) = - \frac{2}{5} x^{\frac{5}{2}} + 32 x^{\frac{1}{2}}

e x t re m e f (x) = (\frac{- 2 x}{x ^{2} + 7})

e x t re m e f (x, y) = (x^{2} - 8 x) (y^{2} - 3 y)

e x t re m e F (x) = \frac{5 x ^{2}}{x ^{2} - 16}