Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Easy proof

  1. Feb 24, 2005 #1
    Please help me prove that it doesn't exist any other intersect point than P(x0, x0^2) on the y=2^2 curve, for the tangent line in the very same point.

    My work:
    y=x^2
    l(x)=f¨(x0)(x-x0)+x0^2
    = 2x0(x-x0)+x0^2
    = 2x0x-2x0^2 + x0^2
    = 2x0x - x0^2
     
  2. jcsd
  3. Feb 24, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    You mean to prove the uniqueness of the tangent to a parabola in one certain (albeit arbitrary) point...?That's trivial.The slope is the same (unique) and they all pass through the same point (namely,the tangence point),therefore,all tangents coincide.

    Unless,you meant something else...

    Daniel.
     
  4. Feb 24, 2005 #3
    Hey, isn't the slope the same in two points (symmetry over the y-axis.) ?

    Edit: Ohh, my no. It's mirrored...
     
    Last edited: Feb 24, 2005
  5. Feb 24, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Yes,it picks up the minus (due to the cosine,which is negative,once you enter [itex] (\pi/2,\pi) [/itex])...

    Daniel.
     
  6. Feb 24, 2005 #5

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    in general a line can only intersect a parabola twice at most and tangent intersections count as 2. done.

    i.e. when you substiotute the parametrization for the loine into the poarabola equation you get a quadratic which can have only 2 roots, and tangents are exactly those points where the root is a double root.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Easy proof
  1. Easy Proof (Replies: 2)

  2. A proof. (Replies: 2)

  3. Sounds easy but (Replies: 3)

Loading...