So I'm beginning numerical analysis and an interesting thing was brought up in class. I know the rules for MVT are:
- $F$ is continuous on $[a,b]$
- $F$ is differentiable on $(a,b)$
So a question was brought up in class I couldn't answer. Why is it that we don't consider differentiability at the end points? The professor sort of assumed we knew the answer but I didn't. My calculus is rusty.
Is there any reason we can't know why the end-points aren't differentiable? A person in class suggested it had to do something with not knowing whats on the other side of the point, but that didn't make any sense to me. Can anyone break this down for me so I can really understand it?