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

Lösung

extrempunkte

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

Minimum (0, 0), Maximum (\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:

Absteigend

: - \infty < x < 0,

Ansteigend

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

Absteigend

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

Stecke

x = 0

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

Minimum (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}}}

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

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