Suppose you have the points $(x_0=0,y_0=0) \quad (x_1=0,y_1=0)$ and the derivative at $x_1$ equal to $0$. How can I find a polynomial of degree 3 that would fit these criterias? I was under the impression that for $P_n$ you needed $n+1$ points, I can imagine graphically how such a polynomial would exist but I am stuck trying to find an algebraic solution.
Points to relevant lit. would be appreciated as well.