extreme x^{2/3}-6x^{-1/3}

Lösung

extrempunkte

x^{\frac{2}{3}} - 6 x^{- \frac{1}{3}}

Minimum (- 3, (- 3)^{\frac{2}{3}} + 2 \cdot 3^{\frac{2}{3}})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - 3

x^{\frac{2}{3}} - 6 x^{- \frac{1}{3}} : (- 3)^{\frac{2}{3}} + 2 \cdot 3^{\frac{2}{3}}

Minimum (- 3, (- 3)^{\frac{2}{3}} + 2 \cdot 3^{\frac{2}{3}})

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

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

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

e x t re m e f (x) = \frac{1}{x}, (- 2, 3)

e x t re m e f (x, y) = y^{3} - x^{2} + 2 x y - 5 y + 5