Results 1 to 7 of 7

Math Help - identify tangent line

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    Vehari
    Posts
    21

    Exclamation identify tangent line

    identify tangent line-identify-tangent.jpg there are two lines AB and CD which one is tangent line and why?

    I know they say AB is tangent line but how to Mathematically( Geometrically(Trigonometrically )) prove it?

    we can take tangent theta too and tangent psi too then both are through tangent of some angle so aren't they both tangent lines?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: identify tangent line

    The curve is smooth and there is only one line that is (locally) entirely on one side of the curve.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2012
    From
    Vehari
    Posts
    21

    Re: identify tangent line

    Good answer to some extent but why isn't CD a tangent line?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,368
    Thanks
    1313

    Re: identify tangent line

    CD is not going in the same direction as the curve at the point where they cross.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member astartleddeer's Avatar
    Joined
    Apr 2012
    From
    England
    Posts
    74
    Thanks
    1

    Re: identify tangent line

    Quote Originally Posted by maddymath View Post
    Good answer to some extent but why isn't CD a tangent line?
    I'd say, if you were to extend  y= f(x) and also the line segment CD. Then the line segment p to D becomes the secant, from which will give the average change until  \lim_{x \to 0} the secant becomes the tangent at point p.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: identify tangent line

    Ah well, let's see what wiki says:

    Quote Originally Posted by wiki
    In geometry, the tangent line (or simply the tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point—that is, coincides with the curve at that point and, near that point, is closer to the curve that any other line passing through that point. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c, f(c)) on the curve and has slope f'(c) where f' is the derivative of f.
    As you can see, CD does not "just touch".

    And if we look at the derivative, we'd be looking at a line through P and a second point on the curve.
    When we let the second point approach P, we get the tangent line.
    This is AB and not CD.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,368
    Thanks
    1313

    Re: identify tangent line

    we can take tangent theta too and tangent psi too then both are through tangent of some angle so aren't they both tangent lines?
    You need to review the definition of "tangent line". It has nothing to do with "tangent of an angle".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 4th 2011, 06:42 PM
  2. Replies: 6
    Last Post: January 12th 2011, 02:38 PM
  3. Replies: 5
    Last Post: November 4th 2009, 06:49 PM
  4. tangent line & normal line question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 15th 2009, 03:45 AM
  5. Replies: 4
    Last Post: March 17th 2008, 01:53 PM

Search Tags


/mathhelpforum @mathhelpforum