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Help finding critical numbers

  1. Oct 19, 2008 #1
    1. The problem statement, all variables and given/known data
    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].


    3. The attempt at a solution
    I found the derivative to be:
    2cos2x

    I need help solving the derivative for 0:
    0=2cos2x
     
  2. jcsd
  3. Oct 19, 2008 #2

    Tom Mattson

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    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?
     
  4. Oct 19, 2008 #3
    that would be pi/2 and 3pi/2. from there do I multiply them by 2?
     
  5. Oct 20, 2008 #4

    HallsofIvy

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    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?
     
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