What is the inflection 1/((3x^2+6)) ?

The inflection 1/((3x^2+6)) is (-sqrt(2/3), 1/8),(sqrt(2/3), 1/8)

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inflection 1/((3x^2+6))

inflection

(- \frac{2}{3}, \frac{1}{8}), (\frac{2}{3}, \frac{1}{8})

Solution steps

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

Find intervals:

Concave Upward

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

Concave Downward

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

Concave Upward

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

Plug

x = - \frac{2}{3}

into

\frac{1}{3 x ^{2} + 6} : \frac{1}{8}

(- \frac{2}{3}, \frac{1}{8})

Plug

x = \frac{2}{3}

into

\frac{1}{3 x ^{2} + 6} : \frac{1}{8}

(\frac{2}{3}, \frac{1}{8})

(- \frac{2}{3}, \frac{1}{8}), (\frac{2}{3}, \frac{1}{8})

What is the inflection 1/((3x^2+6)) ?
The inflection 1/((3x^2+6)) is (-sqrt(2/3), 1/8),(sqrt(2/3), 1/8)