Lagrange's Theorem (thing)

In spite of the name, several theorems are called "Lagrange's". But usually it's one of these:

Group theory:

What Noether noded above. See the proof of Lagrange's theorem for groups.

Calculus:

Let f be a real function which is differentiable on [a,b]. Then for some a<c<b,

        f(a)-f(b)
f'(c) = ---------.
           a-b

If this seems to you like a trivial modification of Rolle's theorem, you're right.