What is the inflection (x^2-9)/(x^2+1) ?

The inflection (x^2-9)/(x^2+1) is (-1/(sqrt(3)),-13/2),(1/(sqrt(3)),-13/2)

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inflection (x^2-9)/(x^2+1)

inflection points

\frac{x ^{2} - 9}{x ^{2} + 1}

(- \frac{1}{3}, - \frac{13}{2}), (\frac{1}{3}, - \frac{13}{2})

Solution steps

f^{''} (x) = \frac{20 ( - 3 x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}

Find intervals:

Concave Downward

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

Concave Upward

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

Concave Downward

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

Plug

x = - \frac{1}{3}

into

\frac{x ^{2} - 9}{x ^{2} + 1} : - \frac{13}{2}

(- \frac{1}{3}, - \frac{13}{2})

Plug

x = \frac{1}{3}

into

\frac{x ^{2} - 9}{x ^{2} + 1} : - \frac{13}{2}

(\frac{1}{3}, - \frac{13}{2})

(- \frac{1}{3}, - \frac{13}{2}), (\frac{1}{3}, - \frac{13}{2})

x^{2} - x

(- 2, 4), (- 6, - 1)

x^{2} - 4 x

f (x) = - 2 x^{3} - 24 x^{2} - 72 x

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

What is the inflection (x^2-9)/(x^2+1) ?
The inflection (x^2-9)/(x^2+1) is (-1/(sqrt(3)),-13/2),(1/(sqrt(3)),-13/2)