LRG G.

asked • 10/22/22

How do I know what values to enter into the appropriate variables?

The questions is "The owner of a clothing manufacturer finds that the total cost of producing 300 of a certain brand of shirts is $2,000, and the marginal cost when 300 shirts are produced is $15 per shirt. Using these numbers, the total cost of producing 302 shirts is approximately [BLANK]"


I'm know that I use the linear approximation L(x) = f(a) + f '(a) (x - a), but I'm not sure what each variable means or what goes to what.

Mark M.

Do you have an example in your text and/or class notes?
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10/22/22

LRG G.

Yes, the question is the same, but the numbers are different. The solution provides no explanation for why they did what they did. It simply displays "C(204) ~ C(200)+C'(200)(204-200)=8,000+35(4)=8,140."
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10/22/22

1 Expert Answer

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LRG G.

Thank you very much. I'm still not sure why the linear approximation is written the way it is or what it means. Could you please explain it to me please?
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10/22/22

Al Y.

tutor
This is simply the linear approximation of a function which states that when x is close to a, then value of function at x can be approximated using a straight line that is tangential to the function (i.e. f'(a)). This is basically a simple case of Taylor's expansion studied in the Calculus. Check out the Wikipedia page for linear approximation.
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10/22/22

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