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

The extreme f(x)=x-sin(x) is Minimum(2pin,2pin-sin(2pin))

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extreme f(x)=x-sin(x)

extreme

Minimum (2 πn, 2 πn - sin (2 πn))

Solution steps

Find the critical points:

x = 2 πn

Domain of

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

Find intervals:

Constant

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

Increasing

: 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

x - sin (x) \Rightarrow y = 2 πn - sin (2 πn)

Minimum (2 πn, 2 πn - sin (2 πn))

What is the extreme f(x)=x-sin(x) ?
The extreme f(x)=x-sin(x) is Minimum(2pin,2pin-sin(2pin))