extreme f(x)=4x^3-6x^2-144x+1

Lösung

extrempunkte

f (x) = 4 x^{3} - 6 x^{2} - 144 x + 1

Maximum (- 3, 271), Minimum (4, - 415)

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 12 x - 144

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = - 3

4 x^{3} - 6 x^{2} - 144 x + 1 : 271

Maximum (- 3, 271)

Stecke

x = 4

4 x^{3} - 6 x^{2} - 144 x + 1 : - 415

Minimum (4, - 415)

Maximum (- 3, 271), Minimum (4, - 415)

e x t re m e f (x, y) = \frac{20480}{x} + \frac{20480}{y} + 5 x y

e x t re m e f (x) = 2 x^{3} + 6 x^{2} - 144 x + 2, - 6 \leq x \leq 5

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

e x t re m e f (x) = (9 sin (x) - 9) (2 cos (x) 3)

e x t re m e f (x) = - x^{3} - 4.5 x^{2} + 12 x - 2