What is the inflection f(x)= 1/(x^2+1) ?

The inflection f(x)= 1/(x^2+1) is (-1/(sqrt(3)), 3/4),(1/(sqrt(3)), 3/4)

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

inflection points

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

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

Solution steps

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

Find intervals:

Concave Upward

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

Concave Downward

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

Concave Upward

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

Plug

x = - \frac{1}{3}

into

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

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

Plug

x = \frac{1}{3}

into

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

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

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

\frac{2}{3} x + 4 - 1

f (x) = x^{2} + x - 2

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

\frac{x + 2}{6}

f (x) = sin (x)

What is the inflection f(x)= 1/(x^2+1) ?
The inflection f(x)= 1/(x^2+1) is (-1/(sqrt(3)), 3/4),(1/(sqrt(3)), 3/4)