extreme x^{2/3}(x-4)

Lösung

extrempunkte

x^{\frac{2}{3}} (x - 4)

Maximum (0, 0), Minimum (\frac{8}{5}, - \frac{48}{5 \cdot 5 ^{\frac{2}{3}}})

Schritte zur Lösung

f^{'} (x) = \frac{5 x - 8}{3 x ^{\frac{1}{3}}}

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{8}{5},

Ansteigend

: \frac{8}{5} < x < \infty

Stecke

x = 0

x^{\frac{2}{3}} (x - 4) : 0

Maximum (0, 0)

Stecke

x = \frac{8}{5}

x^{\frac{2}{3}} (x - 4) : - \frac{48}{5 \cdot 5 ^{\frac{2}{3}}}

Minimum (\frac{8}{5}, - \frac{48}{5 \cdot 5 ^{\frac{2}{3}}})

Maximum (0, 0), Minimum (\frac{8}{5}, - \frac{48}{5 \cdot 5 ^{\frac{2}{3}}})

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

e x t re m e f (x) = x^{5} - 10 x^{4} + 2 = x^{4} (x - 10) + 2

e x t re m e f (x) = x^{9} - x^{7}

e x t re m e 3 x^{4} + 3 y^{4} - 2 x y

e x t re m e f (x) = 150 x + 18 x^{2} - 1.5 x^{3}