What is the inflection f(x)= 4/(x^2+1) ?

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

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inflection f(x)= 4/(x^2+1)

inflection points

f (x) = \frac{4}{x ^{2} + 1}

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

Solution steps

f^{''} (x) = - \frac{8 ( - 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{4}{x ^{2} + 1} : 3

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

Plug

x = \frac{1}{3}

into

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

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

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

f (x) = 6 x^{2} + 9

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

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

- 16 t^{2} + 256

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