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

Lösung

extrempunkte

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

Minimum (0, - 9), Maximum (2, - 5)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 0

- x^{3} + 3 x^{2} - 9 : - 9

Minimum (0, - 9)

Stecke

x = 2

- x^{3} + 3 x^{2} - 9 : - 5

Maximum (2, - 5)

Minimum (0, - 9), Maximum (2, - 5)

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

e x t re m e f (x, y) = 5 x^{2} y^{3} + 4 x^{2} + 5 y

e x t re m e f (x) = 4 x^{3} - 36 x^{2} + 6

e x t re m e f (x) = x^{2} + y^{2} - 14 x + 12 y - 13

e x t re m e f (x) = \frac{( t + 3 ) ^{3}}{( t - 1 ) ^{2}}