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

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

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

inflection points

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

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

Solution steps

f^{''} (x) = - \frac{2 ( - 3 x ^{2} + 1 )}{( 1 + x ^{2} ) ^{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}{1 + x ^{2}} : \frac{3}{4}

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

Plug

x = \frac{1}{3}

into

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

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

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

f (x) = 1 - 5 x

f (x) = \frac{2}{x ^{2} - 9}

f (x) = \frac{2 ( x + 2 )}{x ^{2} - x - 6}

f (x) = 2 x - 1

f (x) = - 3 + 11 x - 4 x^{2}

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