What is the inflection 1/(x^2+10) ?

The inflection 1/(x^2+10) is (-sqrt(10/3), 3/40),(sqrt(10/3), 3/40)

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inflection 1/(x^2+10)

inflection points

\frac{1}{x ^{2} + 10}

(- \frac{10}{3}, \frac{3}{40}), (\frac{10}{3}, \frac{3}{40})

Solution steps

f^{''} (x) = - \frac{2 ( - 3 x ^{2} + 10 )}{( x ^{2} + 10 ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < - \frac{10}{3},

Concave Downward

: - \frac{10}{3} < x < \frac{10}{3},

Concave Upward

: \frac{10}{3} < x < \infty

Plug

x = - \frac{10}{3}

into

\frac{1}{x ^{2} + 10} : \frac{3}{40}

(- \frac{10}{3}, \frac{3}{40})

Plug

x = \frac{10}{3}

into

\frac{1}{x ^{2} + 10} : \frac{3}{40}

(\frac{10}{3}, \frac{3}{40})

(- \frac{10}{3}, \frac{3}{40}), (\frac{10}{3}, \frac{3}{40})

(2) (3)

f (x) = 9

f (x) = \frac{( x ^{2} - 1 )}{( 4 x + 2 )}

f (x) = 2 x^{2} + \frac{256}{x} + 13

\frac{10}{x}

What is the inflection 1/(x^2+10) ?
The inflection 1/(x^2+10) is (-sqrt(10/3), 3/40),(sqrt(10/3), 3/40)