1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Tangent of slope

  1. Aug 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the slope of tangent line to curve that is intersection to the surface z= (x^2) - (y^2) with plane x =2 , at point (2,1,3)
    The ans given by the author is only∂z /∂y = -2

    2. Relevant equations


    3. The attempt at a solution
    Is my diagram correct ?
    I'm wondering , why shouldnt we move the entire graph 'forward ' to x = 2 ?
     

    Attached Files:

    • 361.jpg
      361.jpg
      File size:
      7.5 KB
      Views:
      43
  2. jcsd
  3. Aug 18, 2016 #2

    fresh_42

    Staff: Mentor

    Your diagram is o.k. so far. Except you are right that it should be at ##x=2##.
    Which thoughts brought you to draw it this way. i.e. which equation did you use?
    Next you have to find out, how to calculate a slope at a point. Do you know what this means?
     
  4. Aug 18, 2016 #3
    by looking at the the equation z = 4-(y^2) alone , the whole graph is at x=0 axis alone , right ?
     
  5. Aug 18, 2016 #4

    fresh_42

    Staff: Mentor

    No, it should be at ##x=2## as you've said earlier. But that doesn't change the question, because you have eliminated ##x## in the equation anyway. So you have only a curve in a plane, the same as the usual ##(x,y)## case. The variables simply have different names and all is ##(y,z)## instead. And the slope of a tangent at the curve in a point ##(2,1,3)## is now simply at ##y=1## and ##z=z(y)=4-y^2##.
    You are correct, except you didn't say how to calculate this slope.
     
  6. Aug 18, 2016 #5
    so, the the whole graph is at x = 0 , right ?
    since in z= 4-(y^2) , everything is in z and y , how we know that x = 2 by looking at z= 4-(y^2) ?
     
  7. Aug 18, 2016 #6

    fresh_42

    Staff: Mentor

    No. Originally it's in 3D space with ##(x,y,z)##. The intersection is at ##x=2##. It is like cutting the whole thing along ##x=2##.
    That does not change. But once you have cut it, there is no ##x## anymore. However, you must not forget ##x=2## if further investigations on the original surface would be made, e.g. by comparing the result with a cut at another ##x##.
    As long as the calculations take place with ##x=2## fixed, you may substitute all ##x## by ##2## as you did and forget (for the moment) that there is an ##x## at all. But it stays ##x=2##. We simply do not consider it.

    By looking only at the plane, our cut, there is no ##x## anymore. You can think of it as a parabola with an ##y-## and ##z-## axis. On top of this parabola drawing you note "##\text{Intersection along }x=2##" as its label. Or the more complicated way in a 3D picture like yours, with the ##x-##coordinate ##2##. (As you also already mentioned in your first post.)
     
  8. Aug 18, 2016 #7
    do you mean for z= (x^2) - (y^2) , when x =2 , z= 4 - (y^2) , we draw the curve at x = 0 first , then , extend the line along x-axis and draw another same curve at x = 2?
     

    Attached Files:

  9. Aug 18, 2016 #8

    fresh_42

    Staff: Mentor

    I mean we draw it at ##x=2## in the first place. The question asks about the point ##(2,1,3)## and this point isn't part of anything with ##x=0##.
    Also at ##x=0## the parabola becomes ##z=-y^2## which is shifted by ##4## compared to ##z=4-y^2##.

    In your computer graphic you set ##x=2## as a constant dimension of a 3D space which it is not. A point ##(0,1,-1)## is on the original surface, however, not on the surface of your computer graphic. Have a look how it really looks like:

    http://www.wolframalpha.com/input/?i=z=x^2-y^2
     
  10. Aug 18, 2016 #9
    ok , for the curve at x = 2 , the value of x doesnt change , so ∂z / ∂x = 0 ?
     
  11. Aug 18, 2016 #10

    fresh_42

    Staff: Mentor

    For the curve with ##x=2## there is no ##x## anymore. We substituted it. ##z## is a function of ##y## alone.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Tangent of slope
  1. Slope of tangent (Replies: 12)

Loading...