Consider the function f(n) = 18n 2 − 2n 2 log (n) + 5n 3 which represents the complexity of some algorithm. (a) Find the smallest nonnegative integer p for which n p is a tight big-O bound on f(n). Be sure to justify any inequalities you use and provide the C and k from the big-O definition. (b) Find the largest nonnegative integer p for which n p is a tight big-Ω bound on f(n). Be sure to justify any inequalities you use and provide the C and k from the definition. (c) Based on your work in parts (a) and (b), what is the order of f? (d) Verify that your answer in part (c) is correct by computing any relevant limits. Show all work.