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For example people who are abnormal or who do not have every functions like us.

More generally, if x0 is a point in the domain of a function f, then f is said to bedifferentiable at x0 if the derivative f ′(x0) exists. This means that the graph of f has a non-vertical tangent line at the point (x0, f(x0)). The function f may also be called locally linear at x0, as it can be well approximated by a linear function near this point.