inflection (6x)/(x^2+4)

Lösung

wendepunkte

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

(- 23, - \frac{3 3}{4}), (0, 0), (23, \frac{3 3}{4})

Schritte zur Lösung

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

Intervalle finden:

Konkav fallend

: - \infty < x < - 23,

Konkav steigend

: - 23 < x < 0,

Konkav fallend

: 0 < x < 23,

Konkav steigend

: 23 < x < \infty

Stecke

x = - 23

\frac{6 x}{x ^{2} + 4} : - \frac{3 3}{4}

(- 23, - \frac{3 3}{4})

Stecke

x = 0

\frac{6 x}{x ^{2} + 4} : 0

(0, 0)

Stecke

x = 23

\frac{6 x}{x ^{2} + 4} : \frac{3 3}{4}

(23, \frac{3 3}{4})

(- 23, - \frac{3 3}{4}), (0, 0), (23, \frac{3 3}{4})

in v erse f (x) = \frac{2 x - 3}{4}

s l o p e y = - 2 x - 1

e x t re m e f (x) = ln (7 - 6 x^{2})

p er i o d i c i t y f (x) = 2 sin (x - \frac{π}{4})

l in e (2, 5), (5, 8)