February 24th, 2011, 04:59 PM  #1 
Newbie Joined: Feb 2011 Posts: 21 Thanks: 0  Need Help! Linear approximation!
The demand function for a product is given by p=f(q)=70? squareroot( q) where p is the price per unit in dollars for q units. Use the linear approximation to approximate the the price when 1224 units are demanded. Solution: We want to approximate f(1224) . From f(q)?L(q)=f(a)+f'(a)(q?a) and the fact that f'(a)= (choices are ( 1/sqrt(a) ,1/(2sqrt(a)), 1/(2sqrt(a)), 1/sqrt(a)) we choose a= From f(1225)= and f'(1225)= we get f(1224) . Hence, the price per unit when 1224 units are demanded is approximately $ . 
February 24th, 2011, 05:25 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Need Help! Liner approximation!
We may use the linear approximation to f(q) by the pointslope formula: With we have so and since and we choose a = 1225. Thus with: and we have: This is very close to the actual value of f(1224). 
February 24th, 2011, 05:43 PM  #3 
Newbie Joined: Feb 2011 Posts: 21 Thanks: 0  Re: Need Help! Linear approximation!
THANK YOU !!!!


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approximation, linear 
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