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

Lösung

extrempunkte

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

Minimum (8, - 4)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 8,

Ansteigend

: 8 < x < \infty

Stecke

x = 8

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

Minimum (8, - 4)

e x t re m e f (x) = x^{2} + 9 x - 9

e x t re m e f (x, y) = x^{2} + y^{2} - 4 x + 17 x - 10 y + 2021

e x t re m e f (x) = 18 x^{2} - 32 y^{2} - 36 x - 128 y - 110

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

e x t re m e f (x) = 16 - x^{2}, - 4 \leq x \leq 4