Critical Numbers and Intervals for f(x)=sin2x over [pi, 2pi]

[renob]

Homework Statement

Find all the critical numbers for f(x)=sin2x and the open intervals on which the function is increasing or decreasing over the interval [pie, 2pie].

The Attempt at a Solution

I found the derivative to be:
2cos2x

I need help solving the derivative for 0:
0=2cos2x

 

[quantumdude]

First consult the unit circle to answer the following question: For what angles in the interval from Pi to 2*Pi is cos(A)=0?

 

[renob]

First consult the unit circle to answer the following question: For what angles in the interval from Pi to 2*Pi is cos(A)=0?

that would be pi/2 and 3pi/2. from there do I multiply them by 2?

 

[HallsofIvy]

2 cos(2x)= 0 is, of course, the same as cos(2x)= 0.

If you let A= 2x, then you have cos(A)= 0 so , as you say, A= pi/2 or 3pi/2.
Now remember that A= 2x.
How would you solve 2x= pi/2 and 2x= 3pi/2?