Does a differentiable function have to be continuous? Explain please.

Question

lgbasallote · Answer

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

precal · Answer

the theorem states that if you can take the derivative of a function it implies that it is continuous.

anonymous · Answer

If it is differentiable, then it is continuous.

A continuous function is not always differentiable...but that was not the question.

precal · Answer

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If a function is continuous it does not implie that it is differentiable.
the absolute function is an example of this because you can not take the derivative at the corner.

anonymous · Answer

the answer is yes.

precal · Answer

Yes, but if you are studying AP calculus (students tend to think that the theorem is an iff case.

anonymous · Answer

You are correct, they tend to think continuity implies differentiability....not true as you stated with your example...cusps would be another good example used in an ap calculus class.

precal · Answer

yes besides the whole point of this website is to communicate about mathematics.
I am always amaze how some people are very good at solving problems in different ways.

anonymous · Answer

yep.