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

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

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

extreme points

f (x) = sin (x) + x

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

Solution steps

Find the critical points:

x = π + 2 πn

Domain of

sin (x) + 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

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

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

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