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User:Editeur24/derivative

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A derivative is not always a slope. Consider thi example f: \R \rightarrow \{0,1\}:

f(x) = 0 if x is rational f(x) =1 if x is irrational

f is discontinuous at all rational x. It is continuous and differnetiable at all irrational x. It does not have a slope anywhere.

Is this correct? Source or proof? Ask Chris Connell.