You need to pick so that no only , but also for all (or in a different definition). and , in fact, work, but your writing does not show that you checked the inequality for other than 1 (and possibly 2).

Yes, you need to prove that . Reasoning by contradiction, youThe second one, I am trying a proof by contradiction (though I was always told to assume the negation of the hypothesis).assumethat the negation is true. By definition of big-O, this means that there are , such that . Note that when you were proving , it was your task to find and to prove . Now, youassumedthe negation, so those and that supposedly validate aregivento you. You, as a state attorney, only need to take this evidence provided by the defense, and say, "Ladies and gentlemen of the jury, the argument that you've just heard is absurd. Indeed, plug and see for yourselves."