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- Wondermath

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

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- Wondermath

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

- schrodinger

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- lgbasallote

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

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

- anonymous

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

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- precal

|dw:1328658896786:dw|
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

the answer is yes.

- precal

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

- anonymous

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

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

yep.

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