extreme y=x(x-1)^5

Lösung

extrempunkte

y = 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 f (x) = x^{3} + 6 x^{2} - 6

e x t re m e f (x, y) = x y + x^{2} + y^{2} - x + y + 17

e x t re m e f (x) = 2 x^{3} - 3 x^{2} - 12 x + 1, - 4 \leq x \leq 5

e x t re m e f (x) = 3 x + 2 cos (x)

e x t re m e f (t) = \frac{t}{t - 4}