extreme y=15xe^{-0.05x}-30

Lösung

extrempunkte

y = 15 x e^{- 0.05 x} - 30

Maximum (20, \frac{300}{e} - 30)

Schritte zur Lösung

f^{'} (x) = - 15 e^{- 0.05 x} (0.05 x - 1)

Intervalle finden:

Ansteigend

: - \infty < x < 20,

Absteigend

: 20 < x < \infty

Stecke

x = 20

15 x e^{- 0.05 x} - 30 : \frac{300}{e} - 30

Maximum (20, \frac{300}{e} - 30)

e x t re m e f (x) = \frac{- 4 x}{x ^{2} + 6}, (0, 6)

e x t re m e f (x) = 2 x^{3} + 15 x^{2} - 36 x + 7, - 6 < x < 2

e x t re m e f (x) = 13 e^{- x}, (0, 4)

e x t re m e - y^{2} + 120 y

e x t re m e f (x) = x - \frac{1}{x} + \frac{2}{x ^{3}}, [0, \infty]