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Example of a Monotonic, Everywhere Differentiable Function on ℝ Whose Derivative Is not Continuous
Manas R. Sahoo
The American Mathematical Monthly
Vol. 120, No. 6 (June–July 2013), pp. 566-568
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.06.566
Page Count: 3
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Abstract We construct an example of a monotonic function which is differentiable everywhere, but the derivative is not continuous. This is done using a nonnegative discontinuous integrable function whose every point is a Lebesgue point.
Copyright the Mathematical Association of America 2013