Uni Calculus help needed.. please help.. 10 pts ;)?

Suppose that there is a b in (1,4) so that f(b) < 6. Then in the interval (2,b) or (b,2) (depending on whether or not b > 2), there must be a c so that f(c) = 6 by the Intermediate Value Theorem. But that contradicts the given information. Therefore there is no b in (1,4) with f(b) < 6.