A manufacturer produces bolts of a fabric with a ﬁxed width. The quantity q of this fabric (measured in metres) that is sold is a function of the selling price p (in dollars per metre), that is q = f(p) for some function f. Then the total revenue earned with selling price p is R(p) = pf(p).

(a) What does it mean to say that f(20) = 10000 and f′(20) = −350?

(b) Assuming these values for f(20) and f′(20), ﬁnd R′(20) and interpret your answer.