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..
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 $R(p)=pf(p)$