What is the inflection 1/(7x^2+2) ?

The inflection 1/(7x^2+2) is (-sqrt(2/21), 3/8),(sqrt(2/21), 3/8)

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inflection 1/(7x^2+2)

inflection points

\frac{1}{7 x ^{2} + 2}

(- \frac{2}{21}, \frac{3}{8}), (\frac{2}{21}, \frac{3}{8})

Solution steps

f^{''} (x) = - \frac{14 ( 2 - 21 x ^{2} )}{( 7 x ^{2} + 2 ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < - \frac{2}{21},

Concave Downward

: - \frac{2}{21} < x < \frac{2}{21},

Concave Upward

: \frac{2}{21} < x < \infty

Plug

x = - \frac{2}{21}

into

\frac{1}{7 x ^{2} + 2} : \frac{3}{8}

(- \frac{2}{21}, \frac{3}{8})

Plug

x = \frac{2}{21}

into

\frac{1}{7 x ^{2} + 2} : \frac{3}{8}

(\frac{2}{21}, \frac{3}{8})

(- \frac{2}{21}, \frac{3}{8}), (\frac{2}{21}, \frac{3}{8})

y = 3 - x^{2}

f (x) = 7 + \frac{1}{5} x

(- \frac{5}{2}, \frac{1}{2}), (- \frac{7}{2}, - \frac{9}{2})

f (x) = \frac{2 x ^{2} - x - 1}{x ^{2} + 9}

f (x) = (16 - t)^{\frac{1}{8}}

What is the inflection 1/(7x^2+2) ?
The inflection 1/(7x^2+2) is (-sqrt(2/21), 3/8),(sqrt(2/21), 3/8)