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

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

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

inflection points

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

(- \frac{2}{3}, \frac{1}{4}), (\frac{2}{3}, \frac{1}{4})

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < - \frac{2}{3},

Concave Upward

: - \frac{2}{3} < x < \frac{2}{3},

Concave Downward

: \frac{2}{3} < x < \infty

Plug

x = - \frac{2}{3}

into

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

(- \frac{2}{3}, \frac{1}{4})

Plug

x = \frac{2}{3}

into

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

(\frac{2}{3}, \frac{1}{4})

(- \frac{2}{3}, \frac{1}{4}), (\frac{2}{3}, \frac{1}{4})

f (x) = \frac{x}{3} - 5

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

y = x^{2} + 2

f (x) = \frac{x + 6}{x ^{2} - 2}

f (x) = ln (x^{2} + 1)

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