inflection 1/(x^2+10)

Lösung

wendepunkte

\frac{1}{x ^{2} + 10}

(- \frac{10}{3}, \frac{3}{40}), (\frac{10}{3}, \frac{3}{40})

Schritte zur Lösung

f^{''} (x) = - \frac{2 ( - 3 x ^{2} + 10 )}{( x ^{2} + 10 ) ^{3}}

Intervalle finden:

Konkav steigend

: - \infty < x < - \frac{10}{3},

Konkav fallend

: - \frac{10}{3} < x < \frac{10}{3},

Konkav steigend

: \frac{10}{3} < x < \infty

Stecke

x = - \frac{10}{3}

\frac{1}{x ^{2} + 10} : \frac{3}{40}

(- \frac{10}{3}, \frac{3}{40})

Stecke

x = \frac{10}{3}

\frac{1}{x ^{2} + 10} : \frac{3}{40}

(\frac{10}{3}, \frac{3}{40})

(- \frac{10}{3}, \frac{3}{40}), (\frac{10}{3}, \frac{3}{40})

(2) (3)

a sy m pt o t es f (x) = 9

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

e x t re m e f (x) = 2 x^{2} + \frac{256}{x} + 13

d o main \frac{10}{x}