Let E be a set of differentiable functions in C[a,b] with uniformly bounded derivatives; i.e., there exists a number M, independent of f in E,
such that |f'(x)|<=M for all x in [a,b] and all f in E.
Show that E is equicontinuous.
Equicontinuity is proven. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.