extreme y=e^{(2-x)}+x^2-x/2

Lösung

extrempunkte

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

Minimum W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4}, e^{- W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{7}{4}} + W_{0} (\frac{e ^{\frac{7}{4}}}{2})^{2} + \frac{1}{16} - \frac{1}{8}

Schritte zur Lösung

f^{'} (x) = - e^{2 - x} + 2 x - \frac{1}{2}

Intervalle finden:

Absteigend

: - \infty < x < W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4},

Ansteigend

: W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4} < x < \infty

Stecke

x = W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4}

e^{2 - x} + x^{2} - \frac{x}{2} : e^{- W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{7}{4}} + W_{0} (\frac{e ^{\frac{7}{4}}}{2})^{2} + \frac{1}{16} - \frac{1}{8}

Minimum W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{1}{4}, e^{- W_{0} (\frac{e ^{\frac{7}{4}}}{2}) + \frac{7}{4}} + W_{0} (\frac{e ^{\frac{7}{4}}}{2})^{2} + \frac{1}{16} - \frac{1}{8}

e x t re m e f (x) = - 6 x^{2} - 9 x y - 7 y^{2} - 99 x - 96 y + 5

e x t re m e P (x, y) = x + y^{2} - 10 x^{2} y^{2} + 9 y^{6}

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

e x t re m e f (x) = t 25 - t^{2}

e x t re m e f (x) = \frac{x + 6}{x ^{2} + 6}