extreme f(x)=x^3-9/2 x^2-54x+12

Lösung

extrempunkte

f (x) = x^{3} - \frac{9}{2} x^{2} - 54 x + 12

Maximum (- 3, \frac{213}{2}), Minimum (6, - 258)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 9 x - 54

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = - 3

x^{3} - \frac{9}{2} x^{2} - 54 x + 12 : \frac{213}{2}

Maximum (- 3, \frac{213}{2})

Stecke

x = 6

x^{3} - \frac{9}{2} x^{2} - 54 x + 12 : - 258

Minimum (6, - 258)

Maximum (- 3, \frac{213}{2}), Minimum (6, - 258)

e x t re m e y = x^{2} - 3 x - 70

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

e x t re m e - x^{3} + 3 x^{2} + 9

e x t re m e f (x) = x^{2} + y^{2} + 6 x - 12 y - 9

e x t re m e f (x) = 2 x e^{x} - 4 x^{3}