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

The extreme f(x)=x+sin(x) is Saddle(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

extreme f(x)=x+sin(x)

extreme

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

Solution steps

Find the critical points:

x = π + 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn \leq x < π + 2 πn,

Increasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = π + 2 πn

into

x + sin (x) \Rightarrow y = π + 2 πn + sin (π + 2 πn)

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

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