extreme 3x^4-8x^3+6x^2

Lösung

extrempunkte

3 x^{4} - 8 x^{3} + 6 x^{2}

Minimum (0, 0), Sattel (1, 1)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} - 24 x^{2} + 12 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = 0

3 x^{4} - 8 x^{3} + 6 x^{2} : 0

Minimum (0, 0)

Stecke

x = 1

3 x^{4} - 8 x^{3} + 6 x^{2} : 1

Sattel (1, 1)

Minimum (0, 0), Sattel (1, 1)

e x t re m e \frac{1}{x ^{2} + 1}

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

e x t re m e f (x, y) = x y^{2} - 16 x^{2} - 2 y^{2}

e x t re m e f (x) = \frac{5}{3} x^{3} + 18 x^{2} - 32 x - 30

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