extreme f(x)=(1+x/5)x^{2/3}

Lösung

extrempunkte

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

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

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - 2

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

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

Stecke

x = 0

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

Minimum (0, 0)

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

e x t re m e 3 x + y

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

e x t re m e f (x) = - x^{2} + 190

e x t re m e f (x) = 28 x - \frac{x ^{2}}{105}

e x t re m e 3^{x - 1}