What is the inflection f(x)= 1/(3x^2+7) ?

The inflection f(x)= 1/(3x^2+7) is (-(sqrt(7))/3 , 3/28),((sqrt(7))/3 , 3/28)

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inflection f(x)= 1/(3x^2+7)

inflection points

f (x) = \frac{1}{3 x ^{2} + 7}

(- \frac{7}{3}, \frac{3}{28}), (\frac{7}{3}, \frac{3}{28})

Solution steps

f^{''} (x) = - \frac{6 ( 7 - 9 x ^{2} )}{( 3 x ^{2} + 7 ) ^{3}}

Find intervals:

Concave Upward

: - \infty < x < - \frac{7}{3},

Concave Downward

: - \frac{7}{3} < x < \frac{7}{3},

Concave Upward

: \frac{7}{3} < x < \infty

Plug

x = - \frac{7}{3}

into

\frac{1}{3 x ^{2} + 7} : \frac{3}{28}

(- \frac{7}{3}, \frac{3}{28})

Plug

x = \frac{7}{3}

into

\frac{1}{3 x ^{2} + 7} : \frac{3}{28}

(\frac{7}{3}, \frac{3}{28})

(- \frac{7}{3}, \frac{3}{28}), (\frac{7}{3}, \frac{3}{28})

x^{2} + x + 1

4 x = 5 y^{2} - 3

f (x) = \frac{2 x + 7}{x - 3}

f (x) = \frac{x + 2}{x ^{2} + x - 12}

f (x) = x - 4

What is the inflection f(x)= 1/(3x^2+7) ?
The inflection f(x)= 1/(3x^2+7) is (-(sqrt(7))/3 , 3/28),((sqrt(7))/3 , 3/28)