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

The inflection f(x)= x/(x^2+4) is (-2sqrt(3),-(sqrt(3))/8),(0,0),(2sqrt(3),(sqrt(3))/8)

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

inflection points

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

(- 23, - \frac{3}{8}), (0, 0), (23, \frac{3}{8})

Solution steps

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

(- 23, - \frac{3}{8})

Plug

x = 0

into

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

(0, 0)

Plug

x = 23

into

\frac{x}{x ^{2} + 4} : \frac{3}{8}

(23, \frac{3}{8})

(- 23, - \frac{3}{8}), (0, 0), (23, \frac{3}{8})

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

y = cos (x)

f (x) = 2^{x} + 5

sin (2 arcsin (- \frac{x}{a}))

x^{3} - 4

What is the inflection f(x)= x/(x^2+4) ?
The inflection f(x)= x/(x^2+4) is (-2sqrt(3),-(sqrt(3))/8),(0,0),(2sqrt(3),(sqrt(3))/8)