Okay, so I have this one problem on my Calculus homework that I'm struggling with. I've thought about it all day long, but I'm not getting anywhere. Here's the problem word for word:

"Two small arches have the shape of parabolas. The first is given by f(x)=1-x^2 for x= [-1, 1] and the second by g(x)= 4 - (x - 4)^2 for x=[2, 6]. A board is placed on top of these arches so it rests on both. What is the slope of the board? Hint: Find the tangent line to y=f(x) that intersects y=g(x) in exactly one point."

I don't really want someone to answer it for me, or I'll never learn. I just need a good shove (a better shove that the "hint" in the book).