inflection (x^2)/(x^2+1)

Lösung

wendepunkte

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

(- \frac{1}{3}, \frac{1}{4}), (\frac{1}{3}, \frac{1}{4})

Schritte zur Lösung

f^{''} (x) = \frac{2 ( - 3 x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

Intervalle finden:

Konkav fallend

: - \infty < x < - \frac{1}{3},

Konkav steigend

: - \frac{1}{3} < x < \frac{1}{3},

Konkav fallend

: \frac{1}{3} < x < \infty

Stecke

x = - \frac{1}{3}

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

(- \frac{1}{3}, \frac{1}{4})

Stecke

x = \frac{1}{3}

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

(\frac{1}{3}, \frac{1}{4})

(- \frac{1}{3}, \frac{1}{4}), (\frac{1}{3}, \frac{1}{4})

a sy m pt o t es \frac{4}{( x - 2 ) ^{3}}

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

s l o p e 2 y = 3 x + 5

in v erse f (x) = 2 + 1 + x - 1

d o main y = x - 8