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

The extreme f(x)=cos(x)-x is Saddle((3pi)/2+2pin,cos((3pi)/2+2pin)-(3pi)/2-2pin)

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extreme f(x)=cos(x)-x

extreme points

f (x) = cos (x) - x

Saddle (\frac{3 π}{2} + 2 πn, cos (\frac{3 π}{2} + 2 πn) - \frac{3 π}{2} - 2 πn)

Solution steps

Find the critical points:

x = \frac{3 π}{2} + 2 πn

Domain of

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

Find intervals:

Decreasing

: 2 πn \leq x < \frac{3 π}{2} + 2 πn,

Decreasing

: \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

cos (x) - x \Rightarrow y = cos (\frac{3 π}{2} + 2 πn) - \frac{3 π}{2} - 2 πn

Saddle (\frac{3 π}{2} + 2 πn, cos (\frac{3 π}{2} + 2 πn) - \frac{3 π}{2} - 2 πn)

What is the extreme f(x)=cos(x)-x ?
The extreme f(x)=cos(x)-x is Saddle((3pi)/2+2pin,cos((3pi)/2+2pin)-(3pi)/2-2pin)