extreme e^{-x^2}-2x^2e^{-x^2}

Lösung

extrempunkte

e^{- x^{2}} - 2 x^{2} e^{- x^{2}}

Minimum (- \frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}}), Maximum (0, 1), Minimum (\frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - \frac{3}{2},

Ansteigend

: - \frac{3}{2} < x < 0,

Absteigend

: 0 < x < \frac{3}{2},

Ansteigend

: \frac{3}{2} < x < \infty

Stecke

x = - \frac{3}{2}

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

Minimum (- \frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}})

Stecke

x = 0

e^{- x^{2}} - 2 x^{2} e^{- x^{2}} : 1

Maximum (0, 1)

Stecke

x = \frac{3}{2}

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

Minimum (\frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}})

Minimum (- \frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}}), Maximum (0, 1), Minimum (\frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}})

e x t re m e f (x, y) = 6 x - x^{2} - 2 y - y^{2} + 5

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

e x t re m e f (x) = x + 7 - x

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

e x t re m e - 5 x^{3} + 2 x^{2} - x + 20