What is the extreme f(x)=2x+cos(2x) ?

The extreme f(x)=2x+cos(2x) is Saddle(pi/4+pin,2(pi/4+pin)+cos(2(pi/4+pin)))

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extreme f(x)=2x+cos(2x)

extreme points

f (x) = 2 x + cos (2 x)

Saddle (\frac{π}{4} + πn, 2 (\frac{π}{4} + πn) + cos (2 (\frac{π}{4} + πn)))

Solution steps

Find the critical points:

x = \frac{π}{4} + πn

Domain of

2 x + cos (2 x) : - \infty < x < \infty

Find intervals:

Increasing

: πn \leq x < \frac{π}{4} + πn,

Increasing

: \frac{π}{4} + πn < x < π + πn

Plug the extreme point

x = \frac{π}{4} + πn

into

2 x + cos (2 x) \Rightarrow y = 2 (\frac{π}{4} + πn) + cos (2 (\frac{π}{4} + πn))

Saddle (\frac{π}{4} + πn, 2 (\frac{π}{4} + πn) + cos (2 (\frac{π}{4} + πn)))

What is the extreme f(x)=2x+cos(2x) ?
The extreme f(x)=2x+cos(2x) is Saddle(pi/4+pin,2(pi/4+pin)+cos(2(pi/4+pin)))