Question 5130
 [quote] P= 2xe^-x where x is measured in hours and p is in millions 
a) find the maximum population and when it occurs - i got 735,758 after 1 hour  [/quote]
 
 dP/dx = P' = 2e^-x - 2xe^-x = 2e^-x(1-x) 
 Since,e^-x > 0, we have dP/dx = 0 -->x =1.

 Note P" = -2e^-x(1-x) -2e^-x = 2e^-x(x-3), so P"(1) < 0.
 By the 2nd derivative test,we see that P has relative max when x = 1.
 And P(1) =0.735759377 *1 million (I really don't care about it)

 Or you use the 1st derivative test by testing P'(1+) < 0 and P'(1-)  > 0.
 
 Kenny