extreme f(x)= 1/4 x^4-4/3 x^3+2x^2

Lösung

extrempunkte

f (x) = \frac{1}{4} x^{4} - \frac{4}{3} x^{3} + 2 x^{2}

Minimum (0, 0), Sattel (2, \frac{4}{3})

Schritte zur Lösung

f^{'} (x) = x^{3} - 4 x^{2} + 4 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = 0

\frac{1}{4} x^{4} - \frac{4}{3} x^{3} + 2 x^{2} : 0

Minimum (0, 0)

Stecke

x = 2

\frac{1}{4} x^{4} - \frac{4}{3} x^{3} + 2 x^{2} : \frac{4}{3}

Sattel (2, \frac{4}{3})

Minimum (0, 0), Sattel (2, \frac{4}{3})

e x t re m e f (λ) = x^{2} - y^{2} - λ (4 x - 7 y - 10)

e x t re m e 5 x^{2}

e x t re m e y = 8 + x - x^{2}

e x t re m e f (x) = - (x + 2)^{5} (x - 4)^{4}

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