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Tangent line

  1. Aug 2, 2013 #1
    1. The problem statement, all variables and given/known data
    A tangent line at point A with coordinate (a,f(a)) of function f(x) intersects f(x) at point B coordinate (b,f(b)) . A vertical line is drawn from point p (a<p<b) and intersects f(x) at C. From C a perpendicular line to the tangent line is drawn which intersect the tangent line at point D with coordinate (q,f(q))

    The tangent line can be described by [itex]y_1(x) =a_1 x+ b_1 [/itex]

    |CD| can be described by [itex]y_2(x) =a_2 x+ b_2 [/itex]

    Express q in terms of [itex]a_1,b_1,a_2,b_2[/itex]

    [Broken]


    2. Relevant equations
    -


    3. The attempt at a solution
    I can find [itex]a_1,b_1,a_2,b_2[/itex] in terms of a, b, f(a) and f(b).

    I can express q in terms of the slope of the tangent:

    [tex]q = p + H \sin(\alpha) \cos(\alpha)[/tex]

    with
    [tex] \alpha = arctan\left( \frac{f(b)-f(a)}{b-a} \right) [/tex]

    [tex] H = f(p) -y_1(p)[/tex]
    and now what?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Aug 2, 2013 #2
    This is a fun Euclidean geometry problem. :biggrin:

    ##a_1q+b_1=a_2q+b_2##. Solve for ##q##.
     
    Last edited by a moderator: May 6, 2017
  4. Aug 2, 2013 #3

    verty

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    Homework Helper

    I wonder if there is a mistake in this question. Expressing q in terms of ##a_1##, ##a_2##, ##a_3## and ##a_4## means we don't need to know what those numbers are.
     
  5. Aug 4, 2013 #4
    I can seriously hit myself against the wall. Thanks man.
     
  6. Aug 4, 2013 #5
    No problem. They threw a lot of unnecessary information out there. It took me a minute too. :tongue:
     
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