Final answer:
The correct constants C and k such that the function f(x)=17x+11 is O(x²) are C=18 and k=1, satisfying the inequality 17|x| + 11 ≤ C|x²| for all x ≥ k.
Step-by-step explanation:
The question is asking to find the constants C and k such that the function f(x) = 17x + 11 is O(x²) ('big O notation' representing the upper bound of the growth rate of the function). To show that f(x) is O(x²), we need to find a positive constant C and a value k such that for all x ≥ k, it holds that |f(x)| ≤ C|x²|. Substituting f(x) into the inequality gives us 17|x| + 11 ≤ C|x²|. It is clear that for x ≥ 1, 17x + 11 is always less than any C times x², if C is chosen large enough. For instance, C = 18 and k = 1 satisfy this inequality because 17x + 11 ≤ 18x² whenever x ≥ 1. Therefore, option (a) C=18,k=1 is the correct answer.