Discuss the below:
Let E be an open and convex subset of R^n and let f in C^1(E).
Q: Show that f satisfies the Lipschitz condition on E if and only if its derivative Df is bounded on E, that is, there exists a constant M => 0 such that the norm of IIDf(x)II =< M for all x in E, where IIDf(x)II is the norm of the linear operator Df(x).