Question

Does uniform continuity on an interval I imply differentiability on I? Why or why not and give an example.

Answer 1

So I have shown that if f is differentiable on I and f' is bounded on I, the f is UC on I.
I don't think the converse to this holds true, but I can't think of an example to back me up.

Answer 2

y=|x|

Answer 3

where is y=|x| continuous ?

Answer 4

Everywhere! But it is not differentiable at x=0. Got it! Thanks. Must need more coffee :)

Answer 5

you got it fast enough :)