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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 7, 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
    I know to use the MVT, but besides that I'm lost.
  2. jcsd
  3. Dec 7, 2011 #2


    Staff: Mentor

    Let h(x) = f(x) - g(x).
    From the assumptions in part a, h(a) = h(b) = 0. Now you can use Rolle's Theorem, a special case of the MVT.
  4. Dec 7, 2011 #3
    I already got it, but thanks, though.
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