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

Lösung

extrempunkte

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

Maximum (0, 0), Minimum (\frac{6}{5}, - \frac{9 \cdot 6 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Schritte zur Lösung

f^{'} (x) = \frac{5 x - 6}{3 x ^{\frac{1}{3}}}

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{6}{5},

Ansteigend

: \frac{6}{5} < x < \infty

Stecke

x = 0

x^{\frac{2}{3}} (x - 3) : 0

Maximum (0, 0)

Stecke

x = \frac{6}{5}

x^{\frac{2}{3}} (x - 3) : - \frac{9 \cdot 6 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}}

Minimum (\frac{6}{5}, - \frac{9 \cdot 6 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Maximum (0, 0), Minimum (\frac{6}{5}, - \frac{9 \cdot 6 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

e x t re m e f (x) = 4 x^{3} - 24 x^{2} + 36 x

e x t re m e x^{3} - 12 x^{2} - 45 x + 8

e x t re m e g (t) = e^{4 t^{3}} x ln (3 t - 1)

e x t re m e x^{2} - y^{2} - 2 x + 4 y + 6

e x t re m e f (x) = x^{3} + y^{3} - 15 x y