Answer:
(a) - 25 boxes per dollar
(b) - 20 boxes per dollar
Step-by-step explanation:
Given that,
Consumer's willing to buy boxes of nails at p dollars per box:
N(p) = 80 - 5p^{2}
(a) Change in price from $2 to $3.
N(2) = 80 - 5(2)^{2}
= 80 - 20
= 60
N(3) = 80 - 5(3)^{2}
= 80 - 45
= 35
Therefore, the average rate of change of demand is
= [N(3) - N(2)] ÷ (3 - 2)
= 35 - 60
= - 25 boxes per dollar.
(b) N(p) = 80 - 5p^{2}
Now, differentiating the above function with respect to p,
N'(p) = -10p
Therefore, the instantaneous rate of change of demand when the price is $2 is calculated as follows:
N'(p) = -10p
N'(2) = -10 × 2
= -20 boxes per dollar
