extreme y=e^x-3e^{-x}-4x

Lösung

extrempunkte

y = e^{x} - 3 e^{- x} - 4 x

Maximum (0, - 2), Minimum (ln (3), - 4 ln (3) + 2)

Schritte zur Lösung

f^{'} (x) = e^{x} + 3 e^{- x} - 4

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < ln (3),

Ansteigend

: ln (3) < x < \infty

Stecke

x = 0

e^{x} - 3 e^{- x} - 4 x : - 2

Maximum (0, - 2)

Stecke

x = ln (3)

e^{x} - 3 e^{- x} - 4 x : - 4 ln (3) + 2

Minimum (ln (3), - 4 ln (3) + 2)

Maximum (0, - 2), Minimum (ln (3), - 4 ln (3) + 2)

e x t re m e f (x) = - 6 x^{3} - 54 x^{2} - 144 x - 90

e x t re m e f (x) = (\frac{x + y - x y}{x - y + x y})

e x t re m e 3 (x + 2) (x - 10)

e x t re m e f (x, y) = 1 - x^{2} - x - 3 y^{2} + y

e x t re m e f (x) = 1.4 t e^{- 2.9 t}