Apparently, in English, we often speak of "Lagrange's" Mean Value Theorem. Why? What's the historical background? Isn't that theorem rather attributed to Cauchy or Rolle?
Of course, I noticed, we often use Cauchy for the "stronger MVT", $$ \frac{f(b)-f(a)}{g(b)-g(a)} = \frac{f'(\xi)}{g'(\xi)} $$ but still I don't get how Lagrange's name got involved.
Perhaps this:
http://abesenyei.web.elte.hu/publications/meanvalue.pdf
could be helppful.