extreme f(x)=e^{14x}+e^{-x}

Lösung

extrempunkte

f (x) = e^{14 x} + e^{- x}

Minimum (- \frac{ln ( 14 )}{15}, \frac{1}{e ^{\frac{14 l n ( 14 )}{15}}} + e^{\frac{l n ( 14 )}{15}})

Schritte zur Lösung

f^{'} (x) = e^{14 x} \cdot 14 - e^{- x}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{15} ln (14),

Ansteigend

: - \frac{1}{15} ln (14) < x < \infty

Stecke

x = - \frac{ln ( 14 )}{15}

e^{14 x} + e^{- x} : \frac{1}{e ^{\frac{14 l n ( 14 )}{15}}} + e^{\frac{l n ( 14 )}{15}}

Minimum (- \frac{ln ( 14 )}{15}, \frac{1}{e ^{\frac{14 l n ( 14 )}{15}}} + e^{\frac{l n ( 14 )}{15}})

e x t re m e f (x) = x^{3} - 9 x^{2} - 21 x + 9

e x t re m e f (x) = 4 x^{2} - x - 5

e x t re m e f (x, y) = x^{2} + 14 x y + y^{2}

e x t re m e f (x) = \frac{27 x ^{2}}{( 1 - x ) ^{3}}

e x t re m e f (x) = 345 x^{2} - 3450 x^{3}, 0 \leq x \leq 0.1