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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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})

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)