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

The inflection f(x)=(2x)/(x^2+1) is (-sqrt(3),-(sqrt(3))/2),(0,0),(sqrt(3),(sqrt(3))/2)

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

inflection points

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

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

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < - 3,

Concave Upward

: - 3 < x < 0,

Concave Downward

: 0 < x < 3,

Concave Upward

: 3 < x < \infty

Plug

x = - 3

into

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

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

Plug

x = 0

into

\frac{2 x}{x ^{2} + 1} : 0

(0, 0)

Plug

x = 3

into

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

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

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

f (x) = - x^{2} + 8 x - 7

f (x) = \frac{3}{x - 2}

3 x^{4} - 4 x^{3} + 2

\frac{x ^{3}}{x ^{2} + 12}

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

What is the inflection f(x)=(2x)/(x^2+1) ?
The inflection f(x)=(2x)/(x^2+1) is (-sqrt(3),-(sqrt(3))/2),(0,0),(sqrt(3),(sqrt(3))/2)