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

The extreme f(x)=x-sin(x) is Minimum(2pin,2pin-sin(2pin))

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extreme f(x)=x-sin(x)

extreme points

f (x) = x - sin (x)

Minimum (2 πn, 2 πn - sin (2 πn))

Solution steps

Find the critical points:

x = 2 πn

Domain of

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

Find intervals:

Constant

: E m pt y I n t er v a l,

Increasing

: 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

x - sin (x) \Rightarrow y = 2 πn - sin (2 πn)

Minimum (2 πn, 2 πn - sin (2 πn))

- 2 x^{2} + 24 x - 72

f (x) = x^{3} - 9 x^{2}

y = - 4 x - 8

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

2 x + y = 6

What is the extreme f(x)=x-sin(x) ?
The extreme f(x)=x-sin(x) is Minimum(2pin,2pin-sin(2pin))