Question

Why rose theorem is continous in closed interval and differentiable in open interval?

Answer 1

In our lectures notes, continuous functions are always defined on closed intervals, and differentiable functions, always on open intervals. For instance, if we want to prove a property of a continuous function, it would go as "Let ff be a continuous function on [a,b]⊂R[a,b]⊂R" .. and for a differentiable function it would be (a,b)(a,b) instead.