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

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

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

inflection

(- \frac{1}{3}, \frac{3}{8}), (\frac{1}{3}, \frac{3}{8})

Solution steps

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

Find intervals:

Concave Upward

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

Concave Downward

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

Concave Upward

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

Plug

x = - \frac{1}{3}

into

\frac{1}{2 x ^{2} + 2} : \frac{3}{8}

(- \frac{1}{3}, \frac{3}{8})

Plug

x = \frac{1}{3}

into

\frac{1}{2 x ^{2} + 2} : \frac{3}{8}

(\frac{1}{3}, \frac{3}{8})

(- \frac{1}{3}, \frac{3}{8}), (\frac{1}{3}, \frac{3}{8})

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