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February 24th, 2011, 04:59 PM   #1
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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

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 $ .
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February 24th, 2011, 05:25 PM   #2
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Re: Need Help! Liner approximation!

We may use the linear approximation to f(q) by the point-slope formula:

With we have so

and since and we choose a = 1225. Thus with:


we have:

This is very close to the actual value of f(1224).
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February 24th, 2011, 05:43 PM   #3
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Re: Need Help! Linear approximation!

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