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A manufacturer produces bolts of a fabric with a fixed width. A quantity $q$ of this fabric (measured in yards) that is sold is a function of the selling price $p$ (in dollars per yard), so we can write $q=f(p)$. Then, the total revenue earned with selling price p is $R(p)=pf(p)$.

Find $R′(30)$, given $f(30)=13000$, and $f′(30)=−450$.

I am very confused at the wording of this question and am stuck..

Peter Ferri
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  • You're given a function $R(p) = p f(p$ and the values $f(30) = 13000$, $f'(30) = -450$. You're asked for $R'(30)$. Do you know any methods for computing the derivative of a product...? –  Oct 24 '18 at 03:14
  • like the product rule? $f'(x)g(x)+f(x)g'(x)$ ? – Peter Ferri Oct 24 '18 at 03:25

1 Answers1

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Given $f(30)=13000$, $f^{\prime}(30)=-450$

From the given information, we can say that

For $30/yd., the company will sell 13000 yards

For $31/yd., the company will sell approximately 450 fewer yards.

Assuming the above values, now try to compute $R^{\prime}(30)$ by using the fact that $R(p)=pf(p)$

Key Flex
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