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

Lösung

extrempunkte

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

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

Schritte zur Lösung

f^{'} (x) = - e^{- x} (x^{2} - 4 x + 2)

Intervalle finden:

Absteigend

: - \infty < x < 2 - 2,

Ansteigend

: 2 - 2 < x < 2 + 2,

Absteigend

: 2 + 2 < x < \infty

Stecke

x = 2 - 2

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

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

Stecke

x = 2 + 2

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

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

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

e x t re m e y = \frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2

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

e x t re m e x^{2} - 10 x

e x t re m e f (x, y) = - x^{2} - y^{2} + 16

e x t re m e f (x) = 3 x^{4} - 294 x^{2} + 5