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Homework Help: If f(a)=g(a) and f(b)-g(b), prove they will have parallel tan lines

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data
    (a) If f and g are differentiable functions on the interval [a,b] with f(a)=g(a) and f(b)=g(b), prove that at some point in the interval [a,b], f and g have parallel tangent lines.

    (b) Prove that the result of part a holds if the assumptions f(a)=g(a) and f(b)=g(b) are relaxed to requiring f(b)-f(a)=g(b)-g(a).


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 4, 2011 #2

    LCKurtz

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    You know the rules. What have you tried?
     
  4. Dec 4, 2011 #3
    I haven't, really. I know that by graphing specific examples I can intuitively confirm that it is true. But I'm struggling on how to rigorously prove it.
     
  5. Dec 4, 2011 #4

    LCKurtz

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    Judging from your recent posts you have recently studied a theorem that has expressions like f(b)-f(a) in it haven't you?
     
  6. Dec 4, 2011 #5
    Mvt?
     
  7. Dec 4, 2011 #6

    LCKurtz

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    Yes. Here's my last hint before hitting the sack: Try applying that theorem to H(x) = f(x) - g(x).
     
  8. Dec 4, 2011 #7
    Should I use f'(c)=(f(b)-f(a))/(b-a) and g'(c)=(g(b)-g(a))/(b-a)? Then how should i relate them to each other? Set them equal?
     
  9. Dec 5, 2011 #8

    HallsofIvy

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    You've already said "f(a)=g(a) and f(b)=g(b)" so it is not necessary to "set them equal", they are equal!
     
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