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

The inflection f(x)=-6/(1+x^2) is (-1/(sqrt(3)),-9/2),(1/(sqrt(3)),-9/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

inflection points

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

(- \frac{1}{3}, - \frac{9}{2}), (\frac{1}{3}, - \frac{9}{2})

Solution steps

f^{''} (x) = \frac{12 ( - 3 x ^{2} + 1 )}{( 1 + x ^{2} ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - \frac{1}{3},

Concave Upward

: - \frac{1}{3} < x < \frac{1}{3},

Concave Downward

: \frac{1}{3} < x < \infty

Plug

x = - \frac{1}{3}

into

- \frac{6}{1 + x ^{2}} : - \frac{9}{2}

(- \frac{1}{3}, - \frac{9}{2})

Plug

x = \frac{1}{3}

into

- \frac{6}{1 + x ^{2}} : - \frac{9}{2}

(\frac{1}{3}, - \frac{9}{2})

(- \frac{1}{3}, - \frac{9}{2}), (\frac{1}{3}, - \frac{9}{2})

What is the inflection f(x)=-6/(1+x^2) ?
The inflection f(x)=-6/(1+x^2) is (-1/(sqrt(3)),-9/2),(1/(sqrt(3)),-9/2)