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

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

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

inflection points

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

(- 3, \frac{2 - 3}{2}), (0, 1), (3, \frac{2 + 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{( x + 1 ) ^{2}}{1 + x ^{2}} : \frac{2 - 3}{2}

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

Plug

x = 0

into

\frac{( x + 1 ) ^{2}}{1 + x ^{2}} : 1

(0, 1)

Plug

x = 3

into

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

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

(- 3, \frac{2 - 3}{2}), (0, 1), (3, \frac{2 + 3}{2})

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