extreme f(x)=2x^3-33x^2+180x+6

Lösung

extrempunkte

f (x) = 2 x^{3} - 33 x^{2} + 180 x + 6

Maximum (5, 331), Minimum (6, 330)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} - 66 x + 180

Intervalle finden:

Ansteigend

: - \infty < x < 5,

Absteigend

: 5 < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = 5

2 x^{3} - 33 x^{2} + 180 x + 6 : 331

Maximum (5, 331)

Stecke

x = 6

2 x^{3} - 33 x^{2} + 180 x + 6 : 330

Minimum (6, 330)

Maximum (5, 331), Minimum (6, 330)

e x t re m e f (x) = (x^{4} - 32 x^{2} - 4)

e x t re m e f (x) = 5 x^{3} e^{- x}, - 1 \leq x \leq 4

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

e x t re m e f (x) = \frac{x ^{3} + 4}{x ^{2}}

e x t re m e f (x) = - x^{2} - y^{2} + 8 x + 6 y