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

The inflection f(x)= 1/(x^2+4) is (-2/(sqrt(3)), 3/16),(2/(sqrt(3)), 3/16)

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

inflection points

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

(- \frac{2}{3}, \frac{3}{16}), (\frac{2}{3}, \frac{3}{16})

Solution steps

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

Find intervals:

Concave Upward

: - \infty < x < - \frac{2}{3},

Concave Downward

: - \frac{2}{3} < x < \frac{2}{3},

Concave Upward

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

\frac{1}{x ^{2} + 4} : \frac{3}{16}

(- \frac{2}{3}, \frac{3}{16})

Plug

x = \frac{2}{3}

into

\frac{1}{x ^{2} + 4} : \frac{3}{16}

(\frac{2}{3}, \frac{3}{16})

(- \frac{2}{3}, \frac{3}{16}), (\frac{2}{3}, \frac{3}{16})

What is the inflection f(x)= 1/(x^2+4) ?
The inflection f(x)= 1/(x^2+4) is (-2/(sqrt(3)), 3/16),(2/(sqrt(3)), 3/16)