c) [Extreme Value Theorem:] We say that a function f is continuous on a set S C R if whenever { } is a sequence in S which converges to some ro E S, we have that {f(In) } converges to f(Io). By modifying the proof of the Extreme Value Theorem show that if K is compact and non- empty, and if f is continuous on K, then there exists a ce K such that f(x)