I have this question in my homework. Its an a multiple choice question and goes as following: Let $f (x) = 3x^3 + 2x + 4$. One has that $O(x^3)$
** the answers have been checked with the teachers note **
C and K are the constants
- $(C,K) = (10,0)$
- $(C,K) = (6,1)$
- $(C,K) = (9, 1)$
- $(C,K) = (12,1)$
- $(C,K) = (3,2)$
- $(C,K) = (5,2)$
I know that $(10,0)$ is false since $K = 1$.
$(6,1)$ I also know is wrong because it's smaller than the statement.
But since $3x^3 + 2x^3 + 4x^3 = 9$, then $(9,1)$ is true.
$(12,1)$ is true because I assume its okay that is bigger just not smaller?
$(3,2)$ is false $(5,2)$ is true.
My question here is :Why is it that $(5,2)$ is true? And can anyone tell me whether my thinking is correct or not?
Thank you for any kind of help
