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!

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