extreme f(x)=(3-x)3^x

Lösung

extrempunkte

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

Maximum (- \frac{1}{ln ( 3 )} + 3, \frac{3 ^{\frac{- 1 + 3 l n ( 3 )}{l n ( 3 )}}}{ln ( 3 )})

Schritte zur Lösung

f^{'} (x) = 3^{x} (- 1 - ln (3) (x - 3))

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1}{ln ( 3 )} + 3,

Absteigend

: - \frac{1}{ln ( 3 )} + 3 < x < \infty

Stecke

x = - \frac{1}{ln ( 3 )} + 3

(3 - x) 3^{x} : \frac{3 ^{\frac{- 1 + 3 l n ( 3 )}{l n ( 3 )}}}{ln ( 3 )}

Maximum (- \frac{1}{ln ( 3 )} + 3, \frac{3 ^{\frac{- 1 + 3 l n ( 3 )}{l n ( 3 )}}}{ln ( 3 )})

e x t re m e f (x) = - x^{3} + 27 x - 62

e x t re m e P (a, c) = a + 7 + c

e x t re m e f (x) = \frac{3}{x ^{2} - 2 x}

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

e x t re m e f (x) = x^{3} - \frac{3}{2} x^{2}, - 1 \leq x \leq 4