inflection-1/(x^2+4)

Lösung

wendepunkte

- \frac{1}{x ^{2} + 4}

(- \frac{2}{3}, - \frac{3}{16}), (\frac{2}{3}, - \frac{3}{16})

Schritte zur Lösung

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

Intervalle finden:

Konkav fallend

: - \infty < x < - \frac{2}{3},

Konkav steigend

: - \frac{2}{3} < x < \frac{2}{3},

Konkav fallend

: \frac{2}{3} < x < \infty

Stecke

x = - \frac{2}{3}

- \frac{1}{x ^{2} + 4} : - \frac{3}{16}

(- \frac{2}{3}, - \frac{3}{16})

Stecke

x = \frac{2}{3}

- \frac{1}{x ^{2} + 4} : - \frac{3}{16}

(\frac{2}{3}, - \frac{3}{16})

(- \frac{2}{3}, - \frac{3}{16}), (\frac{2}{3}, - \frac{3}{16})

e x t re m e f (x) = 12 x^{2} + 2 x^{3}

m o n o t o n e x^{2} + \frac{1}{x}

in v erse \frac{1 - 4 x}{2 x + 7}

d o main x^{2} - x

d o main f (x) = lo g_{2} (3 - ∣ 2 - x ∣)