SOLVED 1. The problem statement, all variables and given/known data Find polynomial of least degree satisfying: p(1)=-1, p'(1)=2, p''(1)=0, p(2)=1, p'(2)=-2 2. Relevant equations In general, a Hermite Polynomial is defined by the following: ∑[f(xi)*hi(x)+f'(xi)*h2i(x)] where: hi(xj)=1 if i=j and 0 otherwise. Similarly with h'2. h'i(x)=0 and h2(x)=0. i.e., they are zero if they are integrated or derived. Here is a page from wolfram with general information: http://mathworld.wolfram.com/HermitesInterpolatingPolynomial.html 3. The attempt at a solution First, I recognized x0=1 and x1=2. I tried to create some third coefficient term in order to satisfy p''(1)=0, but that seems to mean that I would have to make hi(xj) be zero for the second derivative, and I have no idea how to do this. I tried just setting this new h (call it h3) equal to (x)(x-2) when derived twice and integrating (so that h3''=1 for x1 and zero otherwise) but that was a total flop. I'm starting to think that, despite the question's section (it was in the section regarding Hermite Interpolating Polynomials), there is a better way to approach it. Any help would be greatly appreciated.