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)))

f (x) = \frac{1}{3} x^{3} - x^{2} - 3 x + 1

f (x) = \frac{1}{3} x^{3} - x^{2} - 3 x + 4

f (x) = x^{3} - 3 x + 3 x y^{2}

f (x, y) = 2 x^{2} + y^{2} - 3 x

f (x) = - (x + 4)^{3}, - 4 \leq x \leq - 3

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)))