What is the inflection ((x^2))/(7x^2+5) ?

The inflection ((x^2))/(7x^2+5) is (-sqrt(5/21), 1/28),(sqrt(5/21), 1/28)

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inflection ((x^2))/(7x^2+5)

inflection points

\frac{( x ^{2} )}{7 x ^{2} + 5}

(- \frac{5}{21}, \frac{1}{28}), (\frac{5}{21}, \frac{1}{28})

Solution steps

f^{''} (x) = \frac{10 ( 5 - 21 x ^{2} )}{( 7 x ^{2} + 5 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - \frac{5}{21},

Concave Upward

: - \frac{5}{21} < x < \frac{5}{21},

Concave Downward

: \frac{5}{21} < x < \infty

Plug

x = - \frac{5}{21}

into

\frac{x ^{2}}{7 x ^{2} + 5} : \frac{1}{28}

(- \frac{5}{21}, \frac{1}{28})

Plug

x = \frac{5}{21}

into

\frac{x ^{2}}{7 x ^{2} + 5} : \frac{1}{28}

(\frac{5}{21}, \frac{1}{28})

(- \frac{5}{21}, \frac{1}{28}), (\frac{5}{21}, \frac{1}{28})

What is the inflection ((x^2))/(7x^2+5) ?
The inflection ((x^2))/(7x^2+5) is (-sqrt(5/21), 1/28),(sqrt(5/21), 1/28)