What is the inflection f(x)=x+sin(x) ?

The inflection f(x)=x+sin(x) is (2pin,2pin+sin(2pin)),(pi+2pin,pi+2pin+sin(pi+2pin))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

inflection f(x)=x+sin(x)

inflection

(2 πn, 2 πn + sin (2 πn)), (π + 2 πn, π + 2 πn + sin (π + 2 πn))

Solution steps

Find where

f^{''} (x)

is equal to zero or undefined

x = 2 πn, x = π + 2 πn

Identify inflection points not in domain or where

f (x)

is not continuous

Domain of

x + sin (x) : - \infty < x < \infty

All inflection points are in domain and not on domain edges

x = 2 πn, x = π + 2 πn

Find intervals:

Undefined

: E m pt y I n t er v a l,

Concave Downward

: 2 πn < x < π + 2 πn,

Concave Upward

: π + 2 πn < x < 2 π + 2 πn

Plug

x = 2 πn

into

x + sin (x) : 2 πn + sin (2 πn)

(2 πn, 2 πn + sin (2 πn))

Plug

x = π + 2 πn

into

x + sin (x) : π + 2 πn + sin (π + 2 πn)

(π + 2 πn, π + 2 πn + sin (π + 2 πn))

(2 πn, 2 πn + sin (2 πn)), (π + 2 πn, π + 2 πn + sin (π + 2 πn))

What is the inflection f(x)=x+sin(x) ?
The inflection f(x)=x+sin(x) is (2pin,2pin+sin(2pin)),(pi+2pin,pi+2pin+sin(pi+2pin))