A manufacturer produces bolts of a fabric with a fixed width. The quantity 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 result

Question

A manufacturer produces bolts of a fabric with a fixed width. The quantity 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 result