extreme f(x)=e^x(3-x^2)

Lösung

extrempunkte

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

Minimum (- 3, - \frac{6}{e ^{3}}), Maximum (1, 2 e)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 1,

Absteigend

: 1 < x < \infty

Stecke

x = - 3

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

Minimum (- 3, - \frac{6}{e ^{3}})

Stecke

x = 1

e^{x} (3 - x^{2}) : 2 e

Maximum (1, 2 e)

Minimum (- 3, - \frac{6}{e ^{3}}), Maximum (1, 2 e)

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

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

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

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

e x t re m e f (x) = x^{3} - 12 x^{2} - 27 x - 26