Please show steps Demand Suppose customers in a hardware store are willing to bu
ID: 2894962 • Letter: P
Question
Please show steps
Demand Suppose customers in a hardware store are willing to buy N(p) boxes of nails at p dollars per box, as given by N(p) = 80 - 5p^2, 1 lessthanorequalto p lessthanorequalto 4. (a) Find the average rate of change of demand for a change in price from $2 to $3. (b) Find and interpret the instantaneous rate of change of demand when the price is $2. (c) Find the instantaneous rate of change of demand when the price is $3. (d) As the price is increased from S2 to $3, how is demand changing? Is the change to be expected? Explain.Explanation / Answer
a) Avg. rate of change. is = [N(3) - N(2)]/[(3)-(2)] = N(3) - N(2)
= 35 - 60 = -25 units/dollar
b) We need the derivative of N and then plug p = 2 to find instantaneous rate of change
N'(p) = -10p
N'(2) = -10*(2) = -20 units/dollar
C) Put p = 3 in N'(3).
N'(3) = -10*(3) = -30 units/dollar
(d) As the price is increased demand N(p) is clearly seen to be decreasing.