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

The inflection x/(x^2+2) is (-sqrt(6),-(sqrt(3))/(4sqrt(2))),(0,0),(sqrt(6),(sqrt(3))/(4sqrt(2)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inflection x/(x^2+2)

inflection points

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

(- 6, - \frac{3}{4 2}), (0, 0), (6, \frac{3}{4 2})

Solution steps

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

Find intervals:

Concave Downward

: - \infty < x < - 6,

Concave Upward

: - 6 < x < 0,

Concave Downward

: 0 < x < 6,

Concave Upward

: 6 < x < \infty

Plug

x = - 6

into

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

(- 6, - \frac{3}{4 2})

Plug

x = 0

into

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

(0, 0)

Plug

x = 6

into

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

(6, \frac{3}{4 2})

(- 6, - \frac{3}{4 2}), (0, 0), (6, \frac{3}{4 2})

3 x^{2}

f (x) = 3^{x} + 5

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

y = - 2 x^{3}

\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1

What is the inflection x/(x^2+2) ?
The inflection x/(x^2+2) is (-sqrt(6),-(sqrt(3))/(4sqrt(2))),(0,0),(sqrt(6),(sqrt(3))/(4sqrt(2)))