(a) Suppose f : A - B, where A, B C R. Define f has a local maximum at c, where c E A is contained in an open interval / C A. (b) What is a critical number of a function f : A - B? (c) State Fermat's Theorem in full. (d) Give a concrete example of a function which shows that the converse of Fermat's The- orem is NOT true. (The converse of "If P. then Q" is "If Q, then P".) Explain your reasoning