What is the inflection x/(x^2+1) ?

The inflection x/(x^2+1) is (-sqrt(3),-(sqrt(3))/4),(0,0),(sqrt(3),(sqrt(3))/4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inflection x/(x^2+1)

inflection points

\frac{x}{x ^{2} + 1}

(- 3, - \frac{3}{4}), (0, 0), (3, \frac{3}{4})

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < - 3,

Concave Upward

: - 3 < x < 0,

Concave Downward

: 0 < x < 3,

Concave Upward

: 3 < x < \infty

Plug

x = - 3

into

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

(- 3, - \frac{3}{4})

Plug

x = 0

into

\frac{x}{x ^{2} + 1} : 0

(0, 0)

Plug

x = 3

into

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

(3, \frac{3}{4})

(- 3, - \frac{3}{4}), (0, 0), (3, \frac{3}{4})

3 x - 2 y = 8

y = x^{2} + 6 x + 8

y = lo g_{3} (x)

\frac{x + 5}{x ^{2} - 12 x + 35}

What is the inflection x/(x^2+1) ?
The inflection x/(x^2+1) is (-sqrt(3),-(sqrt(3))/4),(0,0),(sqrt(3),(sqrt(3))/4)