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

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

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extreme f(x)=sin(x)

extreme points

f (x) = 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)

\frac{10 ( x - 4 )}{3}

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

f (x) = \frac{x - 11}{x ^{2} - 121}

g (x) = x - 3

f (x) = x^{2} - 4 x - 12

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