Let f be a function, defined and continuous on the entire real line, with the property that for every real number C, there is another real number D such that |x D = f(x) > C. (An informal way to say this is: f(x) as x o. For example, the function f(x) = r has this property- given C, we may take D to C- but the function g(x) = does not.) be Apply the Extreme Value Theorem to show that f is bounded below, and attains its minimum: that is, that there is a real number 3 such that f(3) f(x) for every real number z.