1. The problem statement, all variables and given/known data If f is a real function which is continuous at a element R and if f(a)<M for some M element of R, prove that there is an open interval I containing a such that f(x)<M for all x element of I. 2. Relevant equations Extreme value theorem, intermediate value theorem, definition of continuity 3. The attempt at a solution I have no idea how to solve this.