extreme f(x)=x^3(x-5)^2

Lösung

extrempunkte

f (x) = x^{3} (x - 5)^{2}

Sattel (0, 0), Maximum (3, 108), Minimum (5, 0)

Schritte zur Lösung

f^{'} (x) = 5 x^{2} (x - 5) (x - 3)

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 3,

Absteigend

: 3 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = 0

x^{3} (x - 5)^{2} : 0

Sattel (0, 0)

Stecke

x = 3

x^{3} (x - 5)^{2} : 108

Maximum (3, 108)

Stecke

x = 5

x^{3} (x - 5)^{2} : 0

Minimum (5, 0)

Sattel (0, 0), Maximum (3, 108), Minimum (5, 0)

e x t re m e f (x) = \frac{1}{4} x + 3 + \frac{400}{x}

e x t re m e f (x) = cos (x) - x

e x t re m e f (x, y) = x + y + 1

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

e x t re m e f (x) = \frac{x ^{3}}{3} - x^{2} - 3 x