A manufacturer produces bolts of a fabric with a fixed width. The 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).
(a) What does it mean to say that f (20) − 10,000 and f '(20) − 2350?
(b) Assuming the values in part (a), find R'(20) and interpret your answer.