If f ∈ C([a,b]) is differentiable on (a,b) and f(a)=f(b), then ∃c ∈ (a,b) with f'(c)=0. The special case of MVT that Lagrange generalised.
If f ∈ C([a,b]) is differentiable on (a,b) and f(a)=f(b), then ∃c ∈ (a,b) with f'(c)=0. The special case of MVT that Lagrange generalised.