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

The inflection f(x)=(-3)/(x^2+7) is (-sqrt(7/3),-9/28),(sqrt(7/3),-9/28)

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

inflection points

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

(- \frac{7}{3}, - \frac{9}{28}), (\frac{7}{3}, - \frac{9}{28})

Solution steps

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

Find intervals:

Concave Downward

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

Concave Upward

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

Concave Downward

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

Plug

x = - \frac{7}{3}

into

\frac{- 3}{x ^{2} + 7} : - \frac{9}{28}

(- \frac{7}{3}, - \frac{9}{28})

Plug

x = \frac{7}{3}

into

\frac{- 3}{x ^{2} + 7} : - \frac{9}{28}

(\frac{7}{3}, - \frac{9}{28})

(- \frac{7}{3}, - \frac{9}{28}), (\frac{7}{3}, - \frac{9}{28})

f (x) = \frac{2}{5 + x}

(- 3, - 2), (4, 1)

f (x) = - x^{2} - 6 x - 10

(- 2, - 6), (- 5, - 2)

y = x^{2} - 2 x - 3

What is the inflection f(x)=(-3)/(x^2+7) ?
The inflection f(x)=(-3)/(x^2+7) is (-sqrt(7/3),-9/28),(sqrt(7/3),-9/28)