Did you use derivatives or slopes anywhere in your proof? If so, go back and do the proof without them. Two reasons. First, calculus is an absurdly large weapon to use on a problem that can be solved with ordinary algebra. Second, you'll encounter similar problems where some or all of the derivatives don't exist, e.g. functions with integer values. So you need to learn how to do the more basic sort of proof.
Now proceed to checking your outline.