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!

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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: If f(a)=g(a) and f(b)-g(b), prove they will have parallel tan lines
Loading...