extreme e^x+(1-x)/(e^x)

Lösung

extrempunkte

e^{x} + \frac{1 - x}{e ^{x}}

Minimum (- \frac{W _{0} ( 2 e ^{4} ) - 4}{2}, e^{- \frac{W _{0} ( 2 e ^{4} ) - 4}{2}} + \frac{W _{0} ( 2 e ^{4} ) - 2}{2 e ^{- \frac{W _{0} ( 2 e ^{4} ) - 4}{2}}})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < \frac{- W _{0} ( 2 e ^{4} ) + 4}{2},

Ansteigend

: \frac{- W _{0} ( 2 e ^{4} ) + 4}{2} < x < \infty

Stecke

x = - \frac{W _{0} ( 2 e ^{4} ) - 4}{2}

e^{x} + \frac{1 - x}{e ^{x}} : e^{- \frac{W _{0} ( 2 e ^{4} ) - 4}{2}} + \frac{W _{0} ( 2 e ^{4} ) - 2}{2 e ^{- \frac{W _{0} ( 2 e ^{4} ) - 4}{2}}}

Minimum (- \frac{W _{0} ( 2 e ^{4} ) - 4}{2}, e^{- \frac{W _{0} ( 2 e ^{4} ) - 4}{2}} + \frac{W _{0} ( 2 e ^{4} ) - 2}{2 e ^{- \frac{W _{0} ( 2 e ^{4} ) - 4}{2}}})

e x t re m e y = f (x) = x (x - 1)^{5}

e x t re m e y = \frac{e ^{(2 - x)} + x ^{2} - x}{2}

e x t re m e f (x) = 20 (1 + \frac{1}{x} + \frac{1}{x ^{2}})

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

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