Find the largest integer value of n such that n^2-9n+18 is negative.
We want to solve this :
n^2- 9n + 18 < 0 factor the left side
(n - 6) ( n - 3) < 0
Note that this will be true when n is on the interval (3, 6)
So.....the greatest integer value of n that makes the function negative is n = 5
Look at the graph here : https://www.desmos.com/calculator/b3vbllckme
Note that the roots of this polynomial are n = 3 and n = 6
So....at n =6, the polynomial = 0
But we need it to to be negative......so.....the largest integer value to make this true is n = 5
Oh yeah!!! Thanks for the explanation, Chris.
Me to myself: "I didn't realize that this was a polynomial! Read the question, Cal!" LOL!
Anyway, thanks again!