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.
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.