Polynomial nth derivative I was wondering how is this done?
Let $a,b_0,...,b_n \in \mathbb{R}$. 
Show that there exists a polynomial $f(x)$ of degree at most $n$ such that $f(a) = b_0, f'(a) = b_1, f''(a) = b_2, ..., f^{(n)}(a) = b_n$
I can intuitively see that for $x^n$ all the derivatives of it would give a real number when x is a real number, however how do I show what the question is asking for?

Idea: consider a polynomial of the form
$$
p(x) = \sum_{k=0}^n c_k (x-a)^k
$$
and see how the successive derivatives of $p$ at $a$ relate to the $c_k$'s.
