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Math Help - differential problem

  1. #1
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    differential problem

    is there exist a function, which is differentiable in [a,b] but the first derivative is not continuous for some c in (a,b)?
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    Quote Originally Posted by IamLittle View Post
    is there exist a function, which is differentiable in [a,b] but the first derivative is not continuous for some c in (a,b)?
    If a function is differentiable, then it is continuous, but in order for the derivative to exist, it must yield a finite value. If there is some point in (a,b) that causes the first derivative to be discontinuous (e.g not exist), then the function f is not differentiable at that point in [a,b]. So the answer would be no.
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  3. #3
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    but discontinuous not necessarily means that f'(x) is not a finite number, it may also means f'(c)=k but lim X--->c- f'(x) not equal to K
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  4. #4
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    Quote Originally Posted by IamLittle View Post
    is there exist a function, which is differentiable in [a,b] but the first derivative is not continuous for some c in (a,b)?
    http://clem.mscd.edu/~talmanl/PDFs/APCalculus/DiscontDeriv.pdf
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    Super Member Aryth's Avatar
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    That was really useful. Never thought of it that way...
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