extreme xe^{-6x^2}

Lösung

extrempunkte

x e^{- 6 x^{2}}

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

Schritte zur Lösung

f^{'} (x) = - e^{- 6 x^{2}} (23 x + 1) (23 x - 1)

Intervalle finden:

Ansteigend

: - \frac{1}{2 3} < x < \frac{1}{2 3}

Stecke

x = - \frac{1}{2 3}

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

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

Stecke

x = \frac{1}{2 3}

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

Maximum (\frac{1}{2 3}, \frac{1}{2 3 e})

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

e x t re m e f (x) = x^{4} - 8 x^{3} + 10 x^{2} + 1

e x t re m e - 15 x^{4} + 120 x^{2}

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

e x t re m e f (x, y) = \frac{3 x - y}{4}

e x t re m e \frac{x ^{3} + 8}{x}