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#1 2010-02-08 03:26:09
- Magister_Asmodeus
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- Registered: 2009-05-24
- Posts: 5
Discontinuous Derivative
Is it possible for the derivative of a function to be discontinuous? Attention! The derivative must be defined at that point, at which the derivative is discontinuous. I would like to see an example (if you believe it is possible) or a proof showing it is impossible.
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#2 2010-02-08 09:50:17
- Ricky
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- Registered: 2005-12-04
- Posts: 3,791
Re: Discontinuous Derivative
The function
Is differentiable at the origin, but it's derivative is not continuous there.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#3 2010-02-10 08:27:27
- Magister_Asmodeus
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- Registered: 2009-05-24
- Posts: 5
Re: Discontinuous Derivative
How can you say f(0)=0? zero is not in the domain of f. As a result, 0 is not in the domain of f' either. It has no meaning to check Continuity of a function out of its domain.
Last edited by Magister_Asmodeus (2010-02-10 08:29:23)
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#4 2010-02-10 09:14:10
- Ricky
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- Registered: 2005-12-04
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Re: Discontinuous Derivative
It is a piece-wise definition. I was being a bit informal before, so here is the actual definition:
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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