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:

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))

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

sin (x)

(30 cos (3 5^{\circ}), 30 sin (3 5^{\circ})), (0, 0)

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

(- 8, - 4), (6, 5)

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