extreme f(x,y)= 1/3 x^3-x

Lösung

extrempunkte

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

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

Schritte zur Lösung

f^{'} (x) = x^{2} - 1

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

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

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

Stecke

x = 1

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

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

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

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

e x t re m e f (x) = (x^{2} - 1)^{3}, - 1 \leq x \leq 6

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

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

e x t re m e f (x) = - 5 x + 3 ln (4 x)