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′(20), given f(20)=10000, and f′(20)=−350. (What does this mean?)

Question

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′(20), given f(20)=10000, and f′(20)=−350. (What does this mean?)

anonymous · Answer

R'(p)=p*f(p)
$$R'(p) = \frac{d}{dp}R(p)$$
It's asking you to find the derivative of R(p) at p=20
You need to apply the product rule.