inflection x^2e^{-x}

Lösung

wendepunkte

x^{2} e^{- x}

(2 - 2, e^{- 2 + 2} (6 - 42)), (2 + 2, e^{- 2 - 2} (6 + 42))

Schritte zur Lösung

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

Intervalle finden:

Konkav steigend

: - \infty < x < 2 - 2,

Konkav fallend

: 2 - 2 < x < 2 + 2,

Konkav steigend

: 2 + 2 < x < \infty

Stecke

x = 2 - 2

x^{2} e^{- x} : e^{- 2 + 2} (6 - 42)

(2 - 2, e^{- 2 + 2} (6 - 42))

Stecke

x = 2 + 2

x^{2} e^{- x} : e^{- 2 - 2} (6 + 42)

(2 + 2, e^{- 2 - 2} (6 + 42))

(2 - 2, e^{- 2 + 2} (6 - 42)), (2 + 2, e^{- 2 - 2} (6 + 42))

in v erse f (x) = 2 \cdot (\frac{1}{2})^{x}

in v erse f (x) = x + 4 + 9

cr i t i c a l f (x) = (x + 2)^{2} (x - 1)

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

d o main \frac{x ^{3} + x ^{2} - 6 x}{4 x ^{2} + 4 x - 8}