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!

Finding the common tangent?

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi guys, need some help finding the common tangent of two curves.
    Two curves y = 3X3+6X2+6X+3 and y = 3X3+6X+3 touch each other. Find the common tangent.


    2. Relevant equations

    y = 3X3+6X2+6X+3 and y = 3X3+6X+3

    3. The attempt at a solution
    well i made the two equations equal each other and then i found the X values. After that i subbed the values in the the original equations to get my y values. My points ended up being
    (0,3) and (-1,0)

    is the correct? what do i do after this?
    First time with calculus so not sure what to do.
     
  2. jcsd
  3. Feb 15, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi cruisx! :smile:
    (0,3) yes, but how did you get (-1,0) ? :confused:

    anyway, now find the tangent at (0,3). :smile:
     
  4. Feb 15, 2010 #3
    well...um i forget how i got (-1,0) so i only needed to find (0,3)? and then after i find the tangent i am done? I think i got -1,0 because my x values were -1 and 0 so i subbed -1 in to one of my equations to get (-1,0). So i should use (0,3) to find the common tangent?
     
  5. Feb 15, 2010 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Yeah, I guessed that … but how did you get x = -1?

    (I got 6X2 = 0)
    Yes. :smile:
     
  6. Feb 15, 2010 #5
    Hi, so it seems that our next unit is derivatives so i am guessing i will have to find the tangent differently? can someone tell me how to find the tangent using (0,3) because it seems that it has to lead to a derivative or what ever that is. Will find out tomorrow.
     
  7. Feb 16, 2010 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi cruisx! :smile:

    (just got up :zzz: …)
    hmm … without derivatives? :redface:

    ok … try this …

    you know the tangent (to either curve) is a straight line through (0,3),

    so it has to be y = Ax + 3, for some value of A.

    now try a tiny-teeny-weeny value of x (ie very close to 0) in the equation for the curve, and see what for value of A it looks most like y = Ax + 3. :smile:

    (if you prefer, change the cooridnate to y' = y - 3, so the curves meet at the origin)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding the common tangent?
  1. Finding tangent line (Replies: 6)

Loading...