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

The inflection f(x)=(4x)/(x^2+4) is (-2sqrt(3),-(sqrt(3))/2),(0,0),(2sqrt(3),(sqrt(3))/2)

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

inflection points

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

(- 23, - \frac{3}{2}), (0, 0), (23, \frac{3}{2})

Solution steps

f^{''} (x) = - \frac{8 x ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 23,

Concave Upward

: - 23 < x < 0,

Concave Downward

: 0 < x < 23,

Concave Upward

: 23 < x < \infty

Plug

x = - 23

into

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

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

Plug

x = 0

into

\frac{4 x}{x ^{2} + 4} : 0

(0, 0)

Plug

x = 23

into

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

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

(- 23, - \frac{3}{2}), (0, 0), (23, \frac{3}{2})

y = tan (x^{2})

y = - 2 x + 6

\frac{10 x ^{2}}{x ^{4} + 25}

f (x) = 3 - x - x^{2} - 1

\frac{2 x}{- 9 x ^{2} + 324}

What is the inflection f(x)=(4x)/(x^2+4) ?
The inflection f(x)=(4x)/(x^2+4) is (-2sqrt(3),-(sqrt(3))/2),(0,0),(2sqrt(3),(sqrt(3))/2)