extreme y=x^4-x^3

Lösung

extrempunkte

y = x^{4} - x^{3}

Sattel (0, 0), Minimum (\frac{3}{4}, - \frac{27}{256})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{3}{4},

Ansteigend

: \frac{3}{4} < x < \infty

Stecke

x = 0

x^{4} - x^{3} : 0

Sattel (0, 0)

Stecke

x = \frac{3}{4}

x^{4} - x^{3} : - \frac{27}{256}

Minimum (\frac{3}{4}, - \frac{27}{256})

Sattel (0, 0), Minimum (\frac{3}{4}, - \frac{27}{256})

e x t re m e f (x) = 6 x - 12

e x t re m e f (x) = 6 x^{3} - 9 x^{2} - 216 x + 7

e x t re m e f (x, y) = 121 - x^{2} - y^{2}

e x t re m e f (x, y) = x^{3} - 5 x^{2} + 3 y^{2} + 3 x + 1

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