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February 21st, 2012, 11:22 PM   #1
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Differentials and Linear Approximation

Hey guys, I was working hard lately and understanding the new material my teacher had handed out, but I came across this one question and I am stuck. Can anyone please help me?

Question: Suppose the wholesale price of a certain brand of medium-sized eggs is related to the weekly supply by the equation

If 25000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of /carton/week, at what rate is the supply falling?

We are given a hint: to find value of when , solve the supply equation for when .

Please help, looking forward to your responses.
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February 21st, 2012, 11:29 PM   #2
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Re: Differentials and Linear Approximation

I forgot to include my answer:

I needed to rate p wrt t, so i took the whole thing and found


1250p(dp/dt)-2x(dx/dt)=0

dp/dt=[2x(dx/dt)]/1250p

I plugged in 25 for original formula here:
625p^2-(25)^2=100
which came out to

I plugged in that value of P into the other equation:

dp/dt=[2x(dx/dt)]/1250p=[2(25)(-1)]/1250(sqrt(725/625))=-$0.37/week = -$3.7 cents/week


is that correct? and if possible can you show me using latex, i would have submitted mine with latex, but i was tired of fighting latex.
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February 21st, 2012, 11:52 PM   #3
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Re: Differentials and Linear Approximation

I take it that x represents thousands of cartons.

You want to find .

Differentiating the equation relating p and with respect to time t gives:





Now, we are given and when x = 25, and so:



I missed the part where we use a differential to get an approximation.
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