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

Lösung

extrempunkte

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

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

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = 0

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

Maximum (0, 0)

Stecke

x = 2

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

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

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

e x t re m e f (x) = 100 x (2 x + 3) (x - 5)

e x t re m e f (x, y) = 9 - x^{2} + 4 - y^{2}

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

e x t re m e f (x) = 2 x^{3} - 6 x, 0 \leq x \leq 3

e x t re m e \frac{x ^{4}}{x ^{2} - 1}