extreme f(x)=x^{5/3}-12x^{2/3}

Lösung

extrempunkte

f (x) = x^{\frac{5}{3}} - 12 x^{\frac{2}{3}}

Maximum (0, 0), Minimum (\frac{24}{5}, - \frac{144 \cdot 3 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Schritte zur Lösung

f^{'} (x) = \frac{5 x - 24}{3 x ^{\frac{1}{3}}}

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{24}{5},

Ansteigend

: \frac{24}{5} < x < \infty

Stecke

x = 0

x^{\frac{5}{3}} - 12 x^{\frac{2}{3}} : 0

Maximum (0, 0)

Stecke

x = \frac{24}{5}

x^{\frac{5}{3}} - 12 x^{\frac{2}{3}} : - \frac{144 \cdot 3 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}}

Minimum (\frac{24}{5}, - \frac{144 \cdot 3 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Maximum (0, 0), Minimum (\frac{24}{5}, - \frac{144 \cdot 3 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

e x t re m e f (x) = 2 x^{2} ln (x)

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

e x t re m e f (x) = \frac{4 x ^{2}}{x - 8}

e x t re m e f (x) = - 2 x^{2} + 12 x + 3

e x t re m e f (x, y) = 2 x^{2} + 3 y^{2} + 2 x y + 10 x - 20 y