extreme f(x)=x^6(x-4)^5

Lösung

extrempunkte

f (x) = x^{6} (x - 4)^{5}

Maximum (0, 0), Minimum (\frac{24}{11}, - \frac{6.1153 E 14}{1 1 ^{11}}), Sattel (4, 0)

Schritte zur Lösung

f^{'} (x) = x^{5} (x - 4)^{4} (11 x - 24)

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{24}{11},

Ansteigend

: \frac{24}{11} < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 0

x^{6} (x - 4)^{5} : 0

Maximum (0, 0)

Stecke

x = \frac{24}{11}

x^{6} (x - 4)^{5} : - \frac{6.1153 E 14}{1 1 ^{11}}

Minimum (\frac{24}{11}, - \frac{6.1153 E 14}{1 1 ^{11}})

Stecke

x = 4

x^{6} (x - 4)^{5} : 0

Sattel (4, 0)

Maximum (0, 0), Minimum (\frac{24}{11}, - \frac{6.1153 E 14}{1 1 ^{11}}), Sattel (4, 0)

e x t re m e P (q, s) = q + 8 + s

e x t re m e f (x) = (x - 6) \cdot (3 x + 3)

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

e x t re m e f (x, y) = 3 x^{3} - 9 x + 9 x y^{2}

e x t re m e ln (x + 2) (x - 1)^{2}