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

Lösung

extrempunkte

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

Maximum (- \frac{1}{3}, \frac{5}{27}), Minimum (1, - 1)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 2 x - 1

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1}{3},

Absteigend

: - \frac{1}{3} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - \frac{1}{3}

x^{3} - x^{2} - x : \frac{5}{27}

Maximum (- \frac{1}{3}, \frac{5}{27})

Stecke

x = 1

x^{3} - x^{2} - x : - 1

Minimum (1, - 1)

Maximum (- \frac{1}{3}, \frac{5}{27}), Minimum (1, - 1)

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

e x t re m e f (x, y) = \frac{1}{x - y}

e x t re m e f (x, y) = x^{3} + 3 x y^{2} - 15 x - 12 y + 3

e x t re m e y = x^{5} - 5 x^{3} - 20 x - 2

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