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

Lösung

extrempunkte

f (x) = e^{x} - 2 e^{- x} - 3 x

Maximum (0, - 1), Minimum (ln (2), - 3 ln (2) + 1)

Schritte zur Lösung

f^{'} (x) = e^{x} + 2 e^{- x} - 3

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < ln (2),

Ansteigend

: ln (2) < x < \infty

Stecke

x = 0

e^{x} - 2 e^{- x} - 3 x : - 1

Maximum (0, - 1)

Stecke

x = ln (2)

e^{x} - 2 e^{- x} - 3 x : - 3 ln (2) + 1

Minimum (ln (2), - 3 ln (2) + 1)

Maximum (0, - 1), Minimum (ln (2), - 3 ln (2) + 1)

in v erse f (x) = (0, 3), (4, 2), (5, - 6)

in v erse f (x) = 4 x^{3} - 3

r an g e f (x) = \frac{3}{2} (\frac{1}{2}) + 1

in v erse f (x) = - \frac{1}{3} x + 2

p er i o d i c i t y f (x) = 2 cos (5 t) - 3 sin (5 t)