extreme x-x^3

Lösung

extrempunkte

x - x^{3}

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

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{3},

Ansteigend

: - \frac{1}{3} < x < \frac{1}{3},

Absteigend

: \frac{1}{3} < x < \infty

Stecke

x = - \frac{1}{3}

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

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

Stecke

x = \frac{1}{3}

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

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

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

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

e x t re m e f (x) = x^{2} + 4 x + 16

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

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

e x t re m e f (x, y) = x^{3} - 6 x y + 8 y^{3}