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

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

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extreme f(x)=x+sin(x)

extreme points

f (x) = x + sin (x)

Saddle (π + 2 πn, π + 2 πn + sin (π + 2 πn))

Solution steps

Find the critical points:

x = π + 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn \leq x < π + 2 πn,

Increasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = π + 2 πn

into

x + sin (x) \Rightarrow y = π + 2 πn + sin (π + 2 πn)

Saddle (π + 2 πn, π + 2 πn + sin (π + 2 πn))

y = 2 - 3 x

5 - (2 y + 3 x) = 4 (x - y)

\frac{x ^{2} - 3 x - 10}{x - 5}

f (x) = \frac{8}{x - 81}

f (x) = x - 2

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