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posted by  shaydudu88 on 10/10/2008 11:22:19 PM  |  status: Closed  |  Earned Karma: 57

hw due plz help

Course Textbook Chapter Problem Needs by
Calculus Calculus and Its Applications (11th) by Schneider, Lay, Joel Goldstein 2.6 N/A N/A
Question Details:
Let f(t) be the amount of oxygen (in suitable units) in a lake t days after sewage is dumped into the lake, and suppose that f(t) is given approximately by

f(t)=1 -

At what time is the oxygen content increasing the fastest? 

Please show me how to do this problem and I will rate you well. Thanks
shayydudududuuddu
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Apprentice
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posted by juangon20 on 10/11/2008 1:46:44 AM  |  status: Live
Asker's Rating: Helpful   
Response Details:
you have to get derive the equation and find when f1(t) = 0 will give you the time that is increasing the fastest.

first rewrite the problem so its easier to derive

f(t)= 1- 10x (t+10)^-1 + 100x (t+10)^-2

f1(t)= 10 x (t+10)^-2 - 200 x (t+10)^-3

then you put it back in fractions, mutilply the first one by t+10 and worry about the top number equal to zero

f1(t)= 10/ (t+10)^2  - 200/ (t+10)^3

f1(t)= 10t -100/(t+10)^3

0= 10t-100

t=10
AIM me if have questions sportjok19
Oracle
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posted by Chris m/s on 10/11/2008 5:27:13 PM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
first find the formula for f ' (t)
f ' (t) =
Now find the formula for f '' (t) to determine when the rate of increase is the fastest.
f '' (t) =
According to the first derivative test, the function f ' (t) has an extreme point when f '' (t) = 0.
 
0 =
solve for t
20(t+10) = 600
t = 20
 
Therefore the oxygen content of the lake is increasing fastest after 20 days.
Thank you.
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