Answer
(a) $f(20) = 10,000$
When the price is $\$20$ per yard, the quantity of fabric that is sold is 10,000 yards.
$f'(20) = -350$
When the price is $\$20$ per yard, the rate of change in quantity of fabric sold with respect to the price is -350 yards.
(b) $R'(20) = 3,000$
When the price is $\$20$ per yard, the rate of change in total revenue with respect to the price is $\$3,000$
Work Step by Step
(a) $f(20) = 10,000$
This means that when the price is $\$20$ per yard, the quantity of fabric that is sold is 10,000 yards.
$f'(20) = -350$
This means that when the price is $\$20$ per yard, the rate of change in quantity of fabric sold with respect to the price is -350 yards.
(b) $R(p) = p~q = p~f(p)$
$R'(p) = f(p)+p~f'(p)$
$R'(20) = f(20)+(20)~f'(20)$
$R'(20) = 10,000+(20)~(-350)$
$R'(20) = 3,000$
When the price is $\$20$ per yard, the rate of change in total revenue with respect to the price is $\$3,000$
