Thread: Mean Value Theorem

I'm not the greatest conceptual thinker and having a hard time starting this problem. Is the mean value theorem applied or will I use something else?


Let and be differentiable functions on [a,b] where (a)=(a) and (b)=(b). Prove that there is at least one value c in (a,b) where the tangent line to at c is parallel to the tangent line to at c.

Look at the function h(x)= f(x)- g(x). Then h is differentiable, h(a)= f(a)- g(a)= 0, and h(b)= f(b)- g(b)= 0. Apply Rolle's theorem (a special case of the mean value theorem) to h.

Thanks for the quick response! I'll go try that right now

After reviewing the problem and looking at my notes, I'm still kind of confused how to apply Rolle's theorem without being given numbers.