Numerical Analysis - Method of Undetermined Co-efficients

Having a lot of trouble with this one, not even sure where to start:

Q3: Use the method of undetermined coefficients to prove that, for two given points $\displaystyle x0, x1$ (different) and any gives values $\displaystyle y0, y1, z0$ and $\displaystyle z1$ there exists a unique polynomial p(x) of degree 3 such that:

$\displaystyle p(x0) = y0; p(x1) = y1; p'(x0) = z0; p'(x1) = z1 .$ [25 marks]

My lecturer has not specified whether or not MATLAB may be used. Is this question possible without it? If so, how do I go about it?

P.S - This **is** the correct forum for this, isn't it?