Complete the following problems. When computing Big-O/Big-2 values, they should be as tight as possible. This means giving 0 (2n) as the solution to every problem will not receive credit (although technically true, it would be meaningless). 1. Consider the function f(n) = 3n' 39n ? + 360n + 20. In order to prove that f(n) is N(ny), we need constants c, no > 0 such that f(n) 2 cn3 for every n 2 no. Show your work for each part. Work should include any steps you performed to solve the problem (eg, derivations, arithmetic, "I entered this _ into Wolfram Alpha"..). (3 points each for 12 total) a. Suppose we fix c = 2.25. What is the smallest integer value of n, that works? b. Suppose we fix c = 3. Now what is the smallest integer value of n, to satisfy the inequality? C. Suppose we want to fix no = 1. Provide some value of c that satisfies the inequality. d. Provide a value of c such that no matter what value n, takes, the inequality cannot be satisfied