Concept explainers
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) = –350?
(b) Assuming the values in part (a), find R'(20) and interpret your answer.
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