Higher order derivative and extrema, theorem.

Question

I wanted ask, maybe someone here can give a site or other source as to where could I find a theorem about higher order derivatives. The conclusion of theorem is as follows: If $f'(x_0)=f''(x_0)=f'''(x_0)=...=f^{(n-1)}(x_0)$ and $f^{n}(x_0)\neq0$ then if $n\neq2k, \,$where $ k\in N$, $x_0$ is not local extrema. If $n=2k$ and $f^{(n)}(x_0)\ge 0$ then $x_0$ is local minimum, if $f^{(n)}(x_0)\le0$ then $x_0$ is local maximum. So there must be a theorem that proves this result, where can I find it?