Expert: Paul Klarreich - 2/21/2009

Question
The spread of a virus is modeled by N=-t^3+12t^2, 0<=t<=12, where N is the number of people infected(hundreds) and t is the time (weeks).

"When will the virus be spreading most rapidly?" I am not sure what the question is asking for. Is it the maximum rate of change? Please respond ASAP. Thank you.

Answer
Questioner:   Romel
Category:  Calculus
Private:  No
 
Subject:  Applications of Derivatives
Question:  The spread of a virus is modeled by N=-t^3+12t^2, 0<=t<=12, where N is the number of people infected(hundreds) and t is the time (weeks).

"When will the virus be spreading most rapidly?" I am not sure what the question is asking for. Is it the maximum rate of change? Please respond ASAP. Thank you.
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Yes, I think the maximum rate of change is the proper interpretation.  So you want the largest value of  N'(t), for which you will look for inflection points:

N' = 3t^2 + 12t,

N'' = 6t + 12.

Now if you set that = 0, you get  t = -2.  But that is not in your specified interval,  [0,12].

Therefore, the maximum will have to be at one of the endpoints.

Try N'(0)  and  N'(12).  Whichever OF THOSE gives you the max is your answer.