2. [12 points] Prove that f(n) = 6n3 - 12n2 - 84n+1221 is (n). 3. [11 points] Prove for any real constants x and y, where y > 0 (n+7x) = O(n). 4. (a) [8 points] Prove that max( x(f(n),g(n)) = (f(n)+g(n)) (b) [8 points] Prove that if f(n) = 0 (g(n)) and 2(n) = 0 (92(n)), then f1(n) + 2(n) = O(91(n) + 92(n)) 5. [8 points] Prove that lg(n!) is O(n lgn).