Question

How do we verify rolles theorem for greatest integer functions?

Answer 1

Let f:[a,b]→R be continuous on [a,b] and differentiable on (a,b).Such that f(a)=f(b) where a and b are some real numbers.Then there exists some c in (a,b)such that f′(c)=0.

But greatest integer function is neither continuous nor differentiable. Hence Rolle's theorem cannot be verified.