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.