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

The inflection (x^2)/(x^2+1) is (-1/(sqrt(3)), 1/4),(1/(sqrt(3)), 1/4)

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

inflection

(- \frac{1}{3}, \frac{1}{4}), (\frac{1}{3}, \frac{1}{4})

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < - \frac{1}{3},

Concave Upward

: - \frac{1}{3} < x < \frac{1}{3},

Concave Downward

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

\frac{x ^{2}}{x ^{2} + 1} : \frac{1}{4}

(- \frac{1}{3}, \frac{1}{4})

Plug

x = \frac{1}{3}

into

\frac{x ^{2}}{x ^{2} + 1} : \frac{1}{4}

(\frac{1}{3}, \frac{1}{4})

(- \frac{1}{3}, \frac{1}{4}), (\frac{1}{3}, \frac{1}{4})

What is the inflection (x^2)/(x^2+1) ?
The inflection (x^2)/(x^2+1) is (-1/(sqrt(3)), 1/4),(1/(sqrt(3)), 1/4)