extreme f(x)=x^4+x^3-9

Lösung

extrempunkte

f (x) = x^{4} + x^{3} - 9

Minimum (- \frac{3}{4}, - \frac{27}{256} - 9), Sattel (0, - 9)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

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

Ansteigend

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

Ansteigend

: 0 < x < \infty

Stecke

x = - \frac{3}{4}

x^{4} + x^{3} - 9 : - \frac{27}{256} - 9

Minimum (- \frac{3}{4}, - \frac{27}{256} - 9)

Stecke

x = 0

x^{4} + x^{3} - 9 : - 9

Sattel (0, - 9)

Minimum (- \frac{3}{4}, - \frac{27}{256} - 9), Sattel (0, - 9)

e x t re m e f (x, y) = x^{3} + y^{3} - 30 x y

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

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

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

e x t re m e - x^{3} - 3 x^{2}