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

Question

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

perl · Answer

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

perl · Answer

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

perl · Answer

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mony01 · Answer

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

perl · Answer

yes thats true

perl · Answer

well , i think it has to be a closed interval

perl · Answer

but yes , it will be integrable

perl · Answer