What is the inflection (8x)/(x^2+1) ?

The inflection (8x)/(x^2+1) is (-sqrt(3),-2sqrt(3)),(0,0),(sqrt(3),2sqrt(3))

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inflection (8x)/(x^2+1)

inflection points

\frac{8 x}{x ^{2} + 1}

(- 3, - 23), (0, 0), (3, 23)

Solution steps

f^{''} (x) = - \frac{16 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{8 x}{x ^{2} + 1} : - 23

(- 3, - 23)

Plug

x = 0

into

\frac{8 x}{x ^{2} + 1} : 0

(0, 0)

Plug

x = 3

into

\frac{8 x}{x ^{2} + 1} : 23

(3, 23)

(- 3, - 23), (0, 0), (3, 23)

f (x) = 4 x^{2} + 9

\frac{1}{x + 5}

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

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

\frac{x}{x - 2}

What is the inflection (8x)/(x^2+1) ?
The inflection (8x)/(x^2+1) is (-sqrt(3),-2sqrt(3)),(0,0),(sqrt(3),2sqrt(3))