In my course there's a paragraph: Taylor polynomial with Lagrange remainder,
The paragraph starts with a theorem (I left out the constraints):
$$ ( \exists \theta \in ]0,1[)(f(a +h) = T_{f,a,n}(a + h) + \frac{h^{n+1}}{(n+1)!}D^{n+1}f(a + \theta h)) $$
With $f$ an $R-R$ function and $a$ and $a + h$ defined over an interval $I$.
And the only other thing in the paragraph is a proof of the above theorem.
Before I'm starting with the proof, could someone please explain the above theorem in human language?
I understand what a Taylor polynomial is, and what it's good for, but I can't turn this into anything that makes sense...