Did anyone here take the Putnam exam this weekend (or administer it)? What did you think?
I had similar problems, also due to B2. Initially I could only get 1/2 in the upper bound, and not 1/8. But an hour later I realized that there was some vital piece of information in my construction that I wasn't using. Namely, I defined F(x) = [itex]\int_0^x f(t) \, dt[/itex], then because F(1)=F(0)=0, we get (by Rolle's theorem) a c in (0,1) such that F'(c)=0=f(c) (the last equality being the FTC), so now we can use the MVT or a local approximation to proceed from here. What I missed - for a very long time - was that c is an extreme point of F!Personally I thought it was a reasonable test. I kinda burned out on the first half though and I screwed up part B. Spent 2 hours on B2 and didn't really work on B4 or B5 at all...
Yes, that's what I meant. So, I'd have scored a 0 on that one, damn!Probably 0 for that problem as the answer isn't particularly hard to guess.
What do you mean by maximal? Do you mean maximal without going to the other side of the hyperbolas?