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

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

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

inflection points

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

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

Solution steps

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

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

Plug

x = \frac{2}{3}

into

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

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

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

(2 - 5 x) x

f (x) = 3 cos (x)

y = - 3 x - 2

y = - 3 x + 5

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