1. The problem statement, all variables and given/known data Decide whether the given function is bounded above or below on the given interval, and which take on their maximum or minimum value. (Notice that ƒ might have these properties even if ƒ is not continuous, and even if the interval** isn't closed) **The interval is (-a-1, a+1), and it is assumed in the problem that a>-1 so that -a-1 < a+1. 2. Relevant equations ƒ(x) = x^2 if x< or = a, a+2 if x>a 3. The attempt at a solution I concluded that the function is in all cases of a>-1 is bounded above and below, and that if a< or =-1/2, then a+2 is the maximum and minimum, or if -1/2< a < or = 0, then a^2 was the minimum, and then that if a> or = 0 then 0 is the minimum. The part where I struggle is with the latter 2 maximum values where, in the answer book, it states that "Since a+2 > (a+1)^2 only when [(-1-√5)/2] < a < [(-1+√5)/2], when a> or = -1/2 the function ƒ has a maximum value only for a< or = [(-1+√5)/2] (the maximum value being a+2)". I simply don't understand how he came up with the first inequality for a. I tried rearranging the inequality between a+2 and (a+1)^2 but i can't figure it out.