What is the extreme y=sin(x) ?

The extreme y=sin(x) is Maximum(pi/2+2pin,1),Minimum((3pi)/2+2pin,-1)

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extreme y=sin(x)

extreme points

y = sin (x)

Maximum (\frac{π}{2} + 2 πn, 1), Minimum (\frac{3 π}{2} + 2 πn, - 1)

Solution steps

Find the critical points:

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Domain of

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

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{2} + 2 πn,

Decreasing

: \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn,

Increasing

: \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{2} + 2 πn

into

sin (x) \Rightarrow y = 1

Maximum (\frac{π}{2} + 2 πn, 1)

Plug the extreme point

x = \frac{3 π}{2} + 2 πn

into

sin (x) \Rightarrow y = - 1

Minimum (\frac{3 π}{2} + 2 πn, - 1)

Maximum (\frac{π}{2} + 2 πn, 1), Minimum (\frac{3 π}{2} + 2 πn, - 1)

g (x, y) = e^{y} (y - x^{2})

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

e^{- (x^{2} + y^{2})}

f (x) = 478 - x

f (x) = 2 x^{2} ln (x) - 15 x^{2}

What is the extreme y=sin(x) ?
The extreme y=sin(x) is Maximum(pi/2+2pin,1),Minimum((3pi)/2+2pin,-1)