This document provides a counterexample to disprove the statement that if the derivative of a function f(x) approaches infinity as x approaches b, then f(x) is not uniformly continuous on the interval (a,b). It explains that for a function to be uniformly continuous on an interval, its derivative must be 0, as the graph would be a flat line. A function with an infinite derivative near b would likely have an exponential distribution rather than a uniform continuous one.