The derivative of a continuous nonconstant function |
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Authors: | M Martelli and M Dang |
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Institution: | Mathematics Department, CSU Fullerton Fullerton, CA 92634, USA |
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Abstract: | Using elementary ideas and techniques, we prove (Theorem 2) that for a nonconstant differentiable function
, a < b, the set S(f) = {x ε a, b] : f'(x) ≠ 0} cannot be negligible. This result remains valid if f fails to be differentiable on a countable subset of a, b]. |
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Keywords: | Derivative Countable Uncountable Covering Negligible |
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