extreme f(x)=9x^{2/3}-x

Lösung

extrempunkte

f (x) = 9 x^{\frac{2}{3}} - x

Minimum (0, 0), Maximum (216, 108)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < \frac{1}{216},

Ansteigend

: \frac{1}{216} < x < \infty

Stecke

x = 0

9 x^{\frac{2}{3}} - x : 0

Minimum (0, 0)

Stecke

x = 216

9 x^{\frac{2}{3}} - x : 108

Maximum (216, 108)

Minimum (0, 0), Maximum (216, 108)

e x t re m e x + 3, 0 < x < 2

e x t re m e f (x) = x + 4 - x

e x t re m e f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} - 7

e x t re m e f (x, y) = e^{y} (4 x^{2} + 2 x y + y^{2} - 6 x - 15)

e x t re m e 2 (x - 1)^{2} + 5