extreme f(x)=x^8(x-3)^7

Lösung

extrempunkte

f (x) = x^{8} (x - 3)^{7}

Maximum (0, 0), Minimum (\frac{8}{5}, - \frac{1.38168 E 13}{5 ^{15}}), Sattel (3, 0)

Schritte zur Lösung

f^{'} (x) = 3 x^{7} (x - 3)^{6} (5 x - 8)

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{8}{5},

Ansteigend

: \frac{8}{5} < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = 0

x^{8} (x - 3)^{7} : 0

Maximum (0, 0)

Stecke

x = \frac{8}{5}

x^{8} (x - 3)^{7} : - \frac{1.38168 E 13}{5 ^{15}}

Minimum (\frac{8}{5}, - \frac{1.38168 E 13}{5 ^{15}})

Stecke

x = 3

x^{8} (x - 3)^{7} : 0

Sattel (3, 0)

Maximum (0, 0), Minimum (\frac{8}{5}, - \frac{1.38168 E 13}{5 ^{15}}), Sattel (3, 0)

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

e x t re m e f (x) = x (15 - 40 + 2 x) (\frac{40}{2} - x)

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

e x t re m e f (x) = (x^{2} - 6 x) (y^{2} - 7 y)

e x t re m e f (x) = - 5 sec (x)