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Finding the absolute maximum and absolute minimum

  1. Oct 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the absolute max and min of

    f(t)=t + cot(t/2) on [pi/4, 7pi/4]

    2. Relevant equations



    3. The attempt at a solution

    I have attempted to find the derivative which I believe is

    1 - csc^2 (t/2) * (t/2) which I can simplify down to cot^2 (t/2) * (t/2)

    Even if that is correct, which I am doubtful of, where do I go from here?

    Thank You!
     
  2. jcsd
  3. Oct 26, 2009 #2

    Dick

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    Why do you think the derivative of t-cot(t/2) is 1-(csc^(t/2))*(t/2)? Better fix that before you try to proceed.
     
  4. Oct 26, 2009 #3
    Okay ive found the derivative of t + cot (t/2) to be

    1 - csc^2(t/2) * 1/2
     
  5. Oct 26, 2009 #4

    Dick

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    That's much better. So do you have any critical points on [pi/4, 7pi/4]?
     
  6. Oct 26, 2009 #5
    Here in lies the problem Dick. Where do you go from here?

    im at sqrt 2 = csc (t/2) from which ive turned into sqrt 2 = 1/sin (t/2)
     
  7. Oct 26, 2009 #6

    Dick

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    That's pretty good progress. Actually possibilities are at sin(t/2)=+/-1/sqrt(2). Can you draw a graph of sin(x) and tell me where sin(x)=+/-1/sqrt(2)? Then put t/2=x. I happen to know sin(pi/4)=1/sqrt(2).
     
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