inflection (x^3)/(x^2-4)

Lösung

wendepunkte

\frac{x ^{3}}{x ^{2} - 4}

(0, 0)

Schritte zur Lösung

f^{''} (x) = \frac{8 x ( x ^{2} + 12 )}{( x ^{2} - 4 ) ^{3}}

Intervalle finden:

Konkav fallend

: - \infty < x < - 2,

Konkav steigend

: - 2 < x < 0,

Konkav fallend

: 0 < x < 2,

Konkav steigend

: 2 < x < \infty

Stecke

x = 0

\frac{x ^{3}}{x ^{2} - 4} : 0

(0, 0)

e x t re m e f (x) = - 64 x^{3} + 12 x + 4

a sy m pt o t es f (x) = \frac{e ^{2 x} - 2}{e ^{2 x} + 1}

s l o p e in t erce pt 5 - \frac{2 y - 2 x}{2} = 4 x + 4

a sy m pt o t es f (x) = \frac{x ^{2} + 5 x + 4}{x ^{2} - 1}

p er i o d i c i t y f (x) = sin (\frac{1}{2} x)