What is the extreme x+cos(x) ?

The extreme x+cos(x) is Saddle(pi/2+2pin, pi/2+2pin+cos(pi/2+2pin))

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extreme x+cos(x)

extreme

Saddle (\frac{π}{2} + 2 πn, \frac{π}{2} + 2 πn + cos (\frac{π}{2} + 2 πn))

Solution steps

Find the critical points:

x = \frac{π}{2} + 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Increasing

: \frac{π}{2} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

x + cos (x) \Rightarrow y = \frac{π}{2} + 2 πn + cos (\frac{π}{2} + 2 πn)

Saddle (\frac{π}{2} + 2 πn, \frac{π}{2} + 2 πn + cos (\frac{π}{2} + 2 πn))

What is the extreme x+cos(x) ?
The extreme x+cos(x) is Saddle(pi/2+2pin, pi/2+2pin+cos(pi/2+2pin))