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))

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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))