The discussion confirms that the tangent function, tan(x), is locally Lipschitz wherever it is defined, despite not being continuously differentiable at certain points. Participants highlight that tan(x) is continuously differentiable in its domain, reinforcing its local Lipschitz property. Additionally, the example of the function x^(1/3) is provided to illustrate a continuous function that is not locally Lipschitz near zero, emphasizing the distinction between continuity and Lipschitz continuity.
PREREQUISITESMathematicians, calculus students, and anyone interested in the properties of continuous and differentiable functions, particularly in the context of Lipschitz continuity.
Not that hard though, e.g.quasar987 said:And following my geometrical intuition, I would say (...) you would have to try hard to find a function that is continuous but not locally lipschitz!