extreme f(x)=(x^4)/4-(x^3)/3-3x^2

Lösung

extrempunkte

f (x) = \frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 3 x^{2}

Minimum (- 2, - \frac{16}{3}), Maximum (0, 0), Minimum (3, - \frac{63}{4})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 2

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 3 x^{2} : - \frac{16}{3}

Minimum (- 2, - \frac{16}{3})

Stecke

x = 0

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 3 x^{2} : 0

Maximum (0, 0)

Stecke

x = 3

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 3 x^{2} : - \frac{63}{4}

Minimum (3, - \frac{63}{4})

Minimum (- 2, - \frac{16}{3}), Maximum (0, 0), Minimum (3, - \frac{63}{4})

e x t re m e f (x) = 2 x + \frac{20}{x}

e x t re m e f (x, y) = x^{3} + y^{2} - 6 x y - 29 x + 18 y + 20

e x t re m e f (x) = x^{2} - 6 x + 13

e x t re m e y = 2 x^{3} - 12 x^{2} + 9

e x t re m e \frac{8}{x} + 2 π x^{2}