extreme f(x)=e^{-x}(x^2-1)

Lösung

extrempunkte

f (x) = e^{- x} (x^{2} - 1)

Minimum (1 - 2, e^{- 1 + 2} (2 - 22)), Maximum (1 + 2, e^{- 1 - 2} (2 + 22))

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 1 - 2,

Ansteigend

: 1 - 2 < x < 1 + 2,

Absteigend

: 1 + 2 < x < \infty

Stecke

x = 1 - 2

e^{- x} (x^{2} - 1) : e^{- 1 + 2} (2 - 22)

Minimum (1 - 2, e^{- 1 + 2} (2 - 22))

Stecke

x = 1 + 2

e^{- x} (x^{2} - 1) : e^{- 1 - 2} (2 + 22)

Maximum (1 + 2, e^{- 1 - 2} (2 + 22))

Minimum (1 - 2, e^{- 1 + 2} (2 - 22)), Maximum (1 + 2, e^{- 1 - 2} (2 + 22))

e x t re m e h (x) = 2 (x - 5)^{3}

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

e x t re m e f (x) = - 5 x^{3} + 15 x + 6

e x t re m e f (x, y) = (x - 5) (30 - 6 x + 4 y) + (y - 12) (80 + 8 x - 7 y)

e x t re m e f (x) = - 0.001 x^{2} + 3.4 x - 40