inflection f(x)=(x^2)/(e^x)

Lösung

wendepunkte

f (x) = \frac{x ^{2}}{e ^{x}}

(2 - 2, \frac{6 - 4 2}{e ^{2 - 2}}), (2 + 2, \frac{6 + 4 2}{e ^{2 + 2}})

Schritte zur Lösung

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

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

\frac{x ^{2}}{e ^{x}} : \frac{6 - 4 2}{e ^{2 - 2}}

(2 - 2, \frac{6 - 4 2}{e ^{2 - 2}})

Stecke

x = 2 + 2

\frac{x ^{2}}{e ^{x}} : \frac{6 + 4 2}{e ^{2 + 2}}

(2 + 2, \frac{6 + 4 2}{e ^{2 + 2}})

(2 - 2, \frac{6 - 4 2}{e ^{2 - 2}}), (2 + 2, \frac{6 + 4 2}{e ^{2 + 2}})

s im pl i f y (10.5) (5.2)

d o main f (x) = \frac{4}{x + 8} \cdot \frac{1}{7 - x}

f (x) = - 4

in v erse y = \frac{x}{x + 8}

d o main y = 2 x + 3