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

Lösung

extrempunkte

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

Maximum (- 2, - 2^{\frac{1}{3}} - \frac{1}{( - 2 ) ^{\frac{2}{3}}})

Schritte zur Lösung

f^{'} (x) = \frac{1}{3 x ^{\frac{2}{3}}} + \frac{2}{3 x ^{\frac{5}{3}}}

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - 2

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

Maximum (- 2, - 2^{\frac{1}{3}} - \frac{1}{( - 2 ) ^{\frac{2}{3}}})

e x t re m e f (x) = \frac{5 x ^{2}}{x ^{2} - 9}

e x t re m e f (x) = (x - 5)^{\frac{3}{4}}

e x t re m e 32 ln (x) - x^{2}

e x t re m e f (x) = x^{3} - 2 x^{2} - 4 x + 1

e x t re m e f (x, y) = 3 x^{2} + 2 y^{2} - 6 x - 4 y + 16