(adsbygoogle = window.adsbygoogle || []).push({}); 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

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

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