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

The inflection f(x)= 1/(6x^2+3) is (-1/(sqrt(6)), 1/4),(1/(sqrt(6)), 1/4)

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

inflection points

f (x) = \frac{1}{6 x ^{2} + 3}

(- \frac{1}{6}, \frac{1}{4}), (\frac{1}{6}, \frac{1}{4})

Solution steps

f^{''} (x) = - \frac{4 ( 1 - 6 x ^{2} )}{3 ( 2 x ^{2} + 1 ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < - \frac{1}{6},

Concave Downward

: - \frac{1}{6} < x < \frac{1}{6},

Concave Upward

: \frac{1}{6} < x < \infty

Plug

x = - \frac{1}{6}

into

\frac{1}{6 x ^{2} + 3} : \frac{1}{4}

(- \frac{1}{6}, \frac{1}{4})

Plug

x = \frac{1}{6}

into

\frac{1}{6 x ^{2} + 3} : \frac{1}{4}

(\frac{1}{6}, \frac{1}{4})

(- \frac{1}{6}, \frac{1}{4}), (\frac{1}{6}, \frac{1}{4})

What is the inflection f(x)= 1/(6x^2+3) ?
The inflection f(x)= 1/(6x^2+3) is (-1/(sqrt(6)), 1/4),(1/(sqrt(6)), 1/4)