A study has determined that interactions at a large social party follow the mathematical progression N(t)=30t-t^2 , where t is the time in minutes since the party began, and N is the number of separate conversations occurring. At what time in a party do the most conversations occur? what is the maximum number of interactions?
The Product Rule
F(x)=f(x)g(x) then F'(x)=f(x)g'(x)+f'(x)g(x)
The Chain Rule for Polynomials
The Attempt at a Solution
So i decided to get the 1st derivative of N(t)=30t-t^2
so now i'm trying to find t when the function equals 0.
t=15 so this is the time since the party began.
now this is the part i'm not so sure of myself, i add the value of t to the 1st function
=225 so yeah i don't understand the result, what does this one equal to? i'm just confused on how to obtain the results i need here.