Must the graph of a derivative that exists everywhere on


an open interval be a connected set?--The example f(x)=(x^2)sin(1/x) for
nonzero x and f(0)=0 is known to have a derivative everywhere. Although the
derivative is discontinuous at x=0, the graph is connected. I'm guessing there
is no example of the graph of the derivative being disconnected as long as it
exists everywhere on an open interval. Does anyone know? Thanks, Rich Peterson
Sacramento

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