extreme (x^2-3)e^x

Lösung

extrempunkte

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

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

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 3

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

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

Stecke

x = 1

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

Minimum (1, - 2 e)

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

e x t re m e f (x, y) = x^{3} + y^{3} + 3 x y + 5

e x t re m e f (x) = \frac{- cos ( 2 x )}{2} - 2 sin (x)

e x t re m e f (x) = x^{4} + 4 x^{2} - 10, - 5 \leq x \leq 2

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

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