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February 21st, 2012, 11:22 PM  #1 
Senior Member Joined: Jan 2012 Posts: 100 Thanks: 0  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 mediumsized 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. 
February 21st, 2012, 11:29 PM  #2 
Senior Member Joined: Jan 2012 Posts: 100 Thanks: 0  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. 
February 21st, 2012, 11:52 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  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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