What is the extreme-(x+sin(x)) ?

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

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extreme-(x+sin(x))

extreme points

- (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:

Decreasing

: 2 πn \leq x < π + 2 πn,

Decreasing

: 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))

(2, - 7), (- 42, - 57)

\frac{x ^{2} - 3 x}{2 x ^{2} + 2 x - 12}

(8, 10), (- 2, - 14)

f (x) = x^{3} - 5 x + 7

(x - 4)^{2}

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