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

Lösung

extrempunkte

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

Maximum (- 1, \frac{5}{3}), Minimum (3, - 9)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 1

\frac{x ^{3}}{3} - x^{2} - 3 x : \frac{5}{3}

Maximum (- 1, \frac{5}{3})

Stecke

x = 3

\frac{x ^{3}}{3} - x^{2} - 3 x : - 9

Minimum (3, - 9)

Maximum (- 1, \frac{5}{3}), Minimum (3, - 9)

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

e x t re m e f (x, y) = 4 x^{2} + 2 y^{2} - 2 x y - 10 y - 2 x

e x t re m e (x - y) (9 - x y)

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

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