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Homework Help: Calculus-Optimization Problems

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data
    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?


    2. Relevant equations
    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
    F(x)=(f(x))^n,then F'(x)=nf'(x)f(x)^n-1


    3. The attempt at a solution

    So i decided to get the 1st derivative of N(t)=30t-t^2
    N'(t)=30-2t
    so now i'm trying to find t when the function equals 0.
    0=30-2t
    -30/-2=t
    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
    N(15)=30(15)-(15)^2
    =450-225
    =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.
     
  2. jcsd
  3. Sep 19, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    225 is N(15). I guess that's the 'maximum number of separate conversations occuring'. I think you've solved the problem.
     
  4. Sep 19, 2010 #3
    lol, see, that is what happens when you doubt yourself all the time like i do hahaha.
     
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