extreme f(x)=(x^3)/3-x^2-3x-1

Lösung

extrempunkte

f (x) = \frac{x ^{3}}{3} - x^{2} - 3 x - 1

Maximum (- 1, \frac{2}{3}), Minimum (3, - 10)

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 - 1 : \frac{2}{3}

Maximum (- 1, \frac{2}{3})

Stecke

x = 3

\frac{x ^{3}}{3} - x^{2} - 3 x - 1 : - 10

Minimum (3, - 10)

Maximum (- 1, \frac{2}{3}), Minimum (3, - 10)

e x t re m e f (x, y) = x^{4} + y^{4} - 16 x y

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

e x t re m e f (x, y) = 3 x^{2} + 10 x y + 7 y^{2} + 3 x y^{2} + 8 x^{2} y

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

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