extreme f(x)=xe^{-5x^2}

Lösung

extrempunkte

f (x) = x e^{- 5 x^{2}}

Minimum (- \frac{1}{10}, - \frac{1}{10 e}), Maximum (\frac{1}{10}, \frac{1}{10 e})

Schritte zur Lösung

f^{'} (x) = - e^{- 5 x^{2}} (10 x + 1) (10 x - 1)

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{10},

Ansteigend

: - \frac{1}{10} < x < \frac{1}{10},

Absteigend

: \frac{1}{10} < x < \infty

Stecke

x = - \frac{1}{10}

x e^{- 5 x^{2}} : - \frac{1}{10 e}

Minimum (- \frac{1}{10}, - \frac{1}{10 e})

Stecke

x = \frac{1}{10}

x e^{- 5 x^{2}} : \frac{1}{10 e}

Maximum (\frac{1}{10}, \frac{1}{10 e})

Minimum (- \frac{1}{10}, - \frac{1}{10 e}), Maximum (\frac{1}{10}, \frac{1}{10 e})

e x t re m e f (x) = x^{3} - 12 x^{2} + 1

e x t re m e 1 - x^{\frac{2}{3}}

e x t re m e f (x, y) = x^{2} - 0.5 y^{2} + 3 x

e x t re m e f (x) = 8 sin (∣ x ∣), - 2 π \leq x \leq 2 π

e x t re m e f (x) = x^{3} - 6 x + 9 x - 2