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February 11th, 2012, 12:15 AM  #1 
Member Joined: Jan 2012 Posts: 43 Thanks: 0  Application Of Derivatives in Commerce and Economics
I couldnt understand this problem. What do we exactly need to do here ? If anyone could help me out... Thanks : The marginal cost function of manufacturing x units of a commodity is 6 + 10x  6x^2 . The total cost of producing one unit of the commodity is Rs. 12 . Find the total and average cost function. Thanks for checking this out. 
February 11th, 2012, 06:21 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Application Of Derivatives in Commerce and Economics
Take the integral to find the total cost, getting total cost = f(x) for some polynomial f(x) with an unknown constant term. Then solve f(1) = 12 to find that constant.

February 12th, 2012, 03:00 AM  #3 
Member Joined: Jan 2012 Posts: 43 Thanks: 0  Re: Application Of Derivatives in Commerce and Economics
Thanks a lot.. I got your solution but I couldn't understand the second part.. that is after finding the total cost.. Thanks 
February 12th, 2012, 04:42 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Application Of Derivatives in Commerce and Economics
Well, what did you get for the first part?

February 12th, 2012, 09:31 AM  #5 
Member Joined: Jan 2012 Posts: 43 Thanks: 0  Re: Application Of Derivatives in Commerce and Economics
Well, the first part that m getting is just the integrated part, that comes to 6x + 5x^2  2x^3 which is the total cost..

February 12th, 2012, 09:33 AM  #6 
Member Joined: Jan 2012 Posts: 43 Thanks: 0  Re: Application Of Derivatives in Commerce and Economics
So is this correct ? 6x + 5x^2  2x^3 = 12x or, 6x  5x^2 + 2x^3 = 0 ? 
February 12th, 2012, 09:35 AM  #7 
Member Joined: Jan 2012 Posts: 43 Thanks: 0  Re: Application Of Derivatives in Commerce and Economics
that is, 2x^2  5x + 6 = 0... I dont know why its getting so tough..though it doesn't seem to be 
February 12th, 2012, 02:48 PM  #8 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Application Of Derivatives in Commerce and Economics
You forgot the constant of integration, which is what lets you solve for f(1) = 12.

February 13th, 2012, 01:24 AM  #9 
Member Joined: Jan 2012 Posts: 43 Thanks: 0  Re: Application Of Derivatives in Commerce and Economics
okay.. thanks 

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application, commerce, derivatives, economics 
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