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Math Help - Question about continuous function

  1. #1
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    Question about continuous function

    For some continuous function f:\mathbb{R}\rightarrow \mathbb{R}, if I know the value of \frac{f'(x)}{f(x)} at some point x=a, does that tell me any information about the value of either f'(a) or f(a)?

    I'm doubting it, but I want to make sure. Say for example I knew that this ratio was irrational. Does that tell me anything about the rationality of f'(a) or f(a)?
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  2. #2
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    Quote Originally Posted by Media_Man View Post
    For some continuous function f:\mathbb{R}\rightarrow \mathbb{R}, if I know the value of \frac{f'(x)}{f(x)} at some point x=a, does that tell me any information about the value of either f'(a) or f(a)?
    If the ratio exists, you know f(a) \not= 0.

    If the ratio were irrational, then at least one of f(a)\text{ or }f'(a) must be irrational.
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