extreme x^3-12x^2-45x+8

Lösung

extrempunkte

x^{3} - 12 x^{2} - 45 x + 8

Maximum (4 - 31, 6231 - 300), Minimum (4 + 31, - 300 - 6231)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 24 x - 45

Intervalle finden:

Ansteigend

: - \infty < x < - 31 + 4,

Absteigend

: - 31 + 4 < x < 31 + 4,

Ansteigend

: 31 + 4 < x < \infty

Stecke

x = 4 - 31

x^{3} - 12 x^{2} - 45 x + 8 : 6231 - 300

Maximum (4 - 31, 6231 - 300)

Stecke

x = 4 + 31

x^{3} - 12 x^{2} - 45 x + 8 : - 300 - 6231

Minimum (4 + 31, - 300 - 6231)

Maximum (4 - 31, 6231 - 300), Minimum (4 + 31, - 300 - 6231)

e x t re m e g (t) = e^{4 t^{3}} x ln (3 t - 1)

e x t re m e x^{2} - y^{2} - 2 x + 4 y + 6

e x t re m e f (x) = x^{3} + y^{3} - 15 x y

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

e x t re m e f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} + 6 x - 7 y