extreme f(x)=x(x-1)^5

Lösung

extrempunkte

f (x) = x (x - 1)^{5}

Minimum (\frac{1}{6}, - \frac{3125}{46656}), Sattel (1, 0)

Schritte zur Lösung

f^{'} (x) = (x - 1)^{4} (6 x - 1)

Intervalle finden:

Absteigend

: - \infty < x < \frac{1}{6},

Ansteigend

: \frac{1}{6} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = \frac{1}{6}

x (x - 1)^{5} : - \frac{3125}{46656}

Minimum (\frac{1}{6}, - \frac{3125}{46656})

Stecke

x = 1

x (x - 1)^{5} : 0

Sattel (1, 0)

Minimum (\frac{1}{6}, - \frac{3125}{46656}), Sattel (1, 0)

e x t re m e 2 x^{2} - 30 x^{2} + 54 x + 2

e x t re m e y = (x - 6) ln (x - 6)

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

e x t re m e p (x) = 12 x^{4} - 62 x^{3} + a x^{2} - 98 x + 30

e x t re m e y = 3 z^{2} - 3 x^{2}