extreme (x^2+2x)e^{-x}

Lösung

extrempunkte

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

Minimum (- 2, e^{2} (2 - 22)), Maximum (2, \frac{2 + 2 2}{e ^{2}})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - 2

(x^{2} + 2 x) e^{- x} : e^{2} (2 - 22)

Minimum (- 2, e^{2} (2 - 22))

Stecke

x = 2

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

Maximum (2, \frac{2 + 2 2}{e ^{2}})

Minimum (- 2, e^{2} (2 - 22)), Maximum (2, \frac{2 + 2 2}{e ^{2}})

e x t re m e - 7 x^{3} + 21 x + 5

e x t re m e 5 x^{2} e^{- x}

e x t re m e \frac{( 3 x - 1 )}{x}

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

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