What is the inflection x/(5+x^2) ?

The inflection x/(5+x^2) is (-sqrt(15),-(sqrt(3))/(4sqrt(5))),(0,0),(sqrt(15),(sqrt(3))/(4sqrt(5)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inflection x/(5+x^2)

inflection points

\frac{x}{5 + x ^{2}}

(- 15, - \frac{3}{4 5}), (0, 0), (15, \frac{3}{4 5})

Solution steps

f^{''} (x) = - \frac{2 x ( - x ^{2} + 15 )}{( x ^{2} + 5 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 15,

Concave Upward

: - 15 < x < 0,

Concave Downward

: 0 < x < 15,

Concave Upward

: 15 < x < \infty

Plug

x = - 15

into

\frac{x}{5 + x ^{2}} : - \frac{3}{4 5}

(- 15, - \frac{3}{4 5})

Plug

x = 0

into

\frac{x}{5 + x ^{2}} : 0

(0, 0)

Plug

x = 15

into

\frac{x}{5 + x ^{2}} : \frac{3}{4 5}

(15, \frac{3}{4 5})

(- 15, - \frac{3}{4 5}), (0, 0), (15, \frac{3}{4 5})

f (x) = - x^{4} + 6 x^{2}

f (x) = \frac{4 ^{y}}{4}

f (x) = - 4 (x - 2)^{2} (x^{2} - 9)

6 x^{4} + 16 x^{3}

f (x) = \frac{2 x}{2 x - 4}

What is the inflection x/(5+x^2) ?
The inflection x/(5+x^2) is (-sqrt(15),-(sqrt(3))/(4sqrt(5))),(0,0),(sqrt(15),(sqrt(3))/(4sqrt(5)))