What is the extreme sin(x)-x ?

The extreme sin(x)-x is Maximum(2pin,sin(2pin)-2pin)

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extreme sin(x)-x

extreme points

sin (x) - x

Maximum (2 πn, sin (2 πn) - 2 πn)

Solution steps

Find the critical points:

x = 2 πn

Domain of

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

Find intervals:

Constant

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

Decreasing

: 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

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

Maximum (2 πn, sin (2 πn) - 2 πn)

f (x, y) = y + 9 - x^{2} - y^{2}

f (x) = - x^{2} + 160 x - 400

x^{2} - 4 x

x^{y}

f (x) = x 3 + x

What is the extreme sin(x)-x ?
The extreme sin(x)-x is Maximum(2pin,sin(2pin)-2pin)