What is the inflection f(x)= 3/(x^2+4) ?

The inflection f(x)= 3/(x^2+4) is (-2/(sqrt(3)), 9/16),(2/(sqrt(3)), 9/16)

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inflection f(x)= 3/(x^2+4)

inflection points

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

(- \frac{2}{3}, \frac{9}{16}), (\frac{2}{3}, \frac{9}{16})

Solution steps

f^{''} (x) = - \frac{6 ( - 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{3}{x ^{2} + 4} : \frac{9}{16}

(- \frac{2}{3}, \frac{9}{16})

Plug

x = \frac{2}{3}

into

\frac{3}{x ^{2} + 4} : \frac{9}{16}

(\frac{2}{3}, \frac{9}{16})

(- \frac{2}{3}, \frac{9}{16}), (\frac{2}{3}, \frac{9}{16})

f (x) = \frac{2}{9} x + \frac{10}{9}

f (x) = 17 x^{4} - 102 x^{2}

f (x) = ln (8 x), x > 0

(1, 5), (2, 3)

(12, 2), (- 5, - 7)

What is the inflection f(x)= 3/(x^2+4) ?
The inflection f(x)= 3/(x^2+4) is (-2/(sqrt(3)), 9/16),(2/(sqrt(3)), 9/16)