extreme f(x)=x^3-9x^2+15x-5

Lösung

extrempunkte

f (x) = x^{3} - 9 x^{2} + 15 x - 5

Maximum (1, 2), Minimum (5, - 30)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 18 x + 15

Intervalle finden:

Ansteigend

: - \infty < x < 1,

Absteigend

: 1 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = 1

x^{3} - 9 x^{2} + 15 x - 5 : 2

Maximum (1, 2)

Stecke

x = 5

x^{3} - 9 x^{2} + 15 x - 5 : - 30

Minimum (5, - 30)

Maximum (1, 2), Minimum (5, - 30)

e x t re m e g (x, y) = x^{2} + y^{2} - x y + 2 y + 1

e x t re m e f (x, y) = 3 x - x^{3} - 2 y^{2} + y^{4}

e x t re m e f (x, y) = x^{2} y^{2} - 5 x^{2} - 8 x y - 5 y^{2}

e x t re m e f (x, y) = 3 y^{2} - 2 y^{3} - 3 x^{2} + 6 x y

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