Does a differentiable function have to be continuous? Explain please.
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No. There are functions that are continuous but aren't differentiable. For example is the function where it looks like a big "V" when graphed. I don't know the theoretical explanation but that's the best I got :D
the theorem states that if you can take the derivative of a function it implies that it is continuous.
If it is differentiable, then it is continuous.
A continuous function is not always differentiable...but that was not the question.