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Determining signs (+/-/0) of derivatives from a polar graph

  1. Apr 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Use the polar graph to determine the signs (+,-,0) of each derivative at the point labeled A.

    2. Relevant equations
    dy/dx=
    dy/dtheta=
    dx/dtheta=
    dr/dtheta=


    3. The attempt at a solution

    Hi people, I need help with this question. See the picture of the graph attached. I'm not sure if I'm over-complicating this question. I attempted to come up with the equation and got r=6cos2theta. I then substituted r=y/sintheta and r=x/costheta separately to eventually get my dy/dtheta and dx/dtheta, which eventually got dy/dx. I assumed that A came from theta=-2pi/3 and then I plugged that in to get my answers. I ended up getting +, +, +, and -. However, my professor gave me the answers +,-,-, and -. Am I over-complicating the problem? Is there a way to just read the graph? Thanks!
     

    Attached Files:

  2. jcsd
  3. Apr 3, 2012 #2
    dy/dx is the easiest one. Just look at point A, then scoot forward a bit on the x-axis. We see that y grew a bit relative to y at point A. So dy/dx is positive. As for dy/dtheta, draw a radius line from the origin through point A. The angle this line makes with the x-axis is theta. So we scoot theta up a bit. We see that a new radius line going from the origin to a point very close to point A (such that theta increases) goes through a point with y less than y at A. So dy/dtheta is negative. Can you use this line of reasoning to figure out the remainder?
     
  4. Apr 3, 2012 #3
    WOW! This makes sooooo much sense now. I understand it completely now. Thanks for taking your time to help me.
     
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