Question

True or False: If a function is continuous on an interval, it is also differentiable on that interval.
If false, justify with example.

Answer 1

This is not true generally. I can produce a counterexample. Y = | x |

Answer 2

y = | x | is continuous everywhere, but is not differentiable at x = 0 (it has a kink)

Answer 3

@perl thanks what about If a function is continuous on an interval, would it be integrable on that interval?

Answer 4

yes thats true

Answer 5

well , i think it has to be a closed interval

Answer 6

but yes , it will be integrable

Answer 7

http://math.stackexchange.com/questions/253447/prove-that-every-continuous-function-is-integrable