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

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

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

extreme points

f (x) = x + cos (x)

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))

f (x) = - 2 x^{2} + 3 x + 7

f (x) = x^{2} - 5 x y + 6 y^{2} + 9 x - 5 y + 6

F (x, z) = x^{3} + z^{3} - 3 x - 3 z

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

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

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