extreme f(x)=x^{2/3}(x+1)

Lösung

extrempunkte

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

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

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{2}{5},

Absteigend

: - \frac{2}{5} < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - \frac{2}{5}

x^{\frac{2}{3}} (x + 1) : \frac{3 ( - \frac{2}{5} ) ^{\frac{2}{3}}}{5}

Maximum - \frac{2}{5}, \frac{3 ( - \frac{2}{5} ) ^{\frac{2}{3}}}{5}

Stecke

x = 0

x^{\frac{2}{3}} (x + 1) : 0

Minimum (0, 0)

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

e x t re m e f (x) = x^{2} + 4 x (\frac{4000}{x ^{2}})

e x t re m e f (x) = (1)^{\frac{1}{3}} \cdot (- 9)

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

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

e x t re m e f (x) = 7 x^{4} - 28 x^{3 + 7}