# Figuring it out

This is just to test the $\LaTeX$ commands. I seem to be able to insert mathematical symbols inside the text, like $f$ , $I$ or $[a,b]$. I should also be able to emulate the display environment. Let us write

$\displaystyle f'(c)=\frac{f(b)-f(c)}{b-a}.$

Yes, that is alright, but I had to align center manually. Can I write something meaningful, like a definition or a theorem, in a way that emphasize it?

Theorem (the mean value theorem) Let $f [a,b] \rightarrow \mathbb{R}$ be a function that is continuous on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$, then there exists a number $c$ in $(a,b)$ such that

$\displaystyle f'(c)=\frac{f(b)-f(c)}{b-a}.$

I think I will have to number my equation manually, like this:

$\displaystyle \frac{g'(c)}{f'(c)}=\frac{f(b)-f(c)}{g(b)-g(a)}. \ (2)$

I guess this is tolerable for now.

That is all!