Wondermath
  • Wondermath
Does a differentiable function have to be continuous? Explain please.
Mathematics
schrodinger
  • schrodinger
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lgbasallote
  • 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
  • precal
the theorem states that if you can take the derivative of a function it implies that it is continuous.
anonymous
  • 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
  • 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
  • anonymous
the answer is yes.
precal
  • precal
Yes, but if you are studying AP calculus (students tend to think that the theorem is an iff case.
anonymous
  • 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
  • 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
  • anonymous
yep.

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