Let f(x)=xp Show that f is Lipschitz on every closed sub-interval [a,b] of (0,inf). For which values of p is f uniformly continuous.
So, we know that the map f is said to be Lipschitz iff there is a constant M s.t. |f(p)-f(q)|<=M|p-q|. And we were given the hint to use the Mean Value...