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Using differentiation to find maximum length problems

  1. Feb 14, 2013 #1
    1. The problem statement, all variables and given/known data

    The line segment AB lies on a diameter of a circle of radius 1, and the angle BAC is a right angle.

    Find the greatest possible value of the sum of the lengths of AB and AC.


    2. Relevant equations



    3. The attempt at a solution

    I have no idea what parameters to use or how to set up the problem.

    Any help would be much appreciated.
     

    Attached Files:

  2. jcsd
  3. Feb 14, 2013 #2

    Dick

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    Why not try picking the parameter to be the x coordinate of A?
     
  4. Feb 14, 2013 #3
    check out the attachment, does that seem right?
     

    Attached Files:

  5. Feb 14, 2013 #4

    Dick

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    Well, you ignored my advice on which parameter to use, so apparently you weren't all that confused to begin with. Yes, it looks ok.
     
  6. Feb 14, 2013 #5
    Haha sorry, I had so many ideas of ways to do it and that's the only one I managed to fully work through :)
     
  7. Feb 15, 2013 #6

    HallsofIvy

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    Here (I think) is what Dick was suggesting: set up a coordinate system so the origin is at the center of the circle, A is at (-1, 0), and the y-axis is parallel to BC. Then AB has length x+ 1 and BC has length [itex]\sqrt{1- x^2}[/itex].
     
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