Suppose that I is an open interval and that f "(x) is greater than or equal to 0 for all x in I. If b is in I, then show that the part of the graph of f on I is never below the tangent line to the graph at (b, f(b)).
Suppose that I is ...
shouldn't it be "Suppose that I am ..."??
If two or more thoughts intersect with each other, then there has to be a point.