extreme y=xe^{-3x^2}

Lösung

extrempunkte

y = x e^{- 3 x^{2}}

Minimum (- \frac{1}{6}, - \frac{1}{6 e}), Maximum (\frac{1}{6}, \frac{1}{6 e})

Schritte zur Lösung

f^{'} (x) = - e^{- 3 x^{2}} (6 x + 1) (6 x - 1)

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{6},

Ansteigend

: - \frac{1}{6} < x < \frac{1}{6},

Absteigend

: \frac{1}{6} < x < \infty

Stecke

x = - \frac{1}{6}

x e^{- 3 x^{2}} : - \frac{1}{6 e}

Minimum (- \frac{1}{6}, - \frac{1}{6 e})

Stecke

x = \frac{1}{6}

x e^{- 3 x^{2}} : \frac{1}{6 e}

Maximum (\frac{1}{6}, \frac{1}{6 e})

Minimum (- \frac{1}{6}, - \frac{1}{6 e}), Maximum (\frac{1}{6}, \frac{1}{6 e})

e x t re m e f (x, y) = 4 x + 5 y

e x t re m e 6 x^{2} - 2 x^{4}

e x t re m e x - 2 ln (x + 1)

e x t re m e f (x, y) = 4 x + 6 y

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