Let f be a convex function on an open set S which is bounded above by M in a neighborhood of x0. That is, there exists an open ball Br(x0) containing x0 such that f is bounded on B(x0). Let x1 be an arbitrary point in S.
1. Show that there exists a number t > 1 such that
z = x0 + t(x1 - x0) ˆˆ S
2. Define

T is a neighborhood of x1.
3. f is bounded above on T.

T = {y e X: y = (1 )x+ az, x E B(xq)}.