Okay, here's what I got for #2...
Now we can tell a few things from the information that they give us from the tangent lines. If the tangent at is , then we know that because the derivative takes the value of the slope of the tangent line. We also know that because is tangent at and . Likewise the other tangent line tells us that and with this information we can start chipping away at the coefficients. Let's start with the derivative:
using this and our other derivative point we find...
this equation of a and b may seem like a dead end, but we'll use it later. Now let's look at the function itself and the points that we have for it. notice that I'm going to continue using c=2.
using this information and the other function point we discover...
lo and behold, we have yet another equation of a and b. Now we can set up a linear system to solve for the last two coefficients:
you can solve this by whatever method suits you, and you'll discover that a=1 and b=-6.
collecting our results: