Question

why we check function to be continuos at boundry points and differentiable in open interval ??​

Answer 1

In general, other intervals do not yield the same properties to continuous functions defined on them. On an open interval every point is an interior point, so this intuition holds fine. If a function is differentiable at the boundary point of a closed interval the graph will locally look like a ray.

Answer 2

Answer:

MARK THE UPPER ONE AS THE BRAINLIEST ☺✌