Suppose customers in a hardware store are willing to buy N(p) boxes of nails at
ID: 2874781 • Letter: S
Question
Suppose customers in a hardware store are willing to buy N(p) boxes of nails at p dollars per box, as given by the following function. N(p) = 70 - 3p^2: 2 lessthanorequalto p lessthanorequalto 5 a. Find the average rate of change of demand for a change in price from $3 to $4. The average rate of change of demand for a change in price from $3 to $4 is boxes per dollar. (Type an integer or a decimal.) b. Find the instantaneous rate of change of demand when the price is $3 The instantaneous rate of change of demand when the price is $3 is boxes per dollar. (Type an integer or a decimal.) c. Find the instantaneous rate of change of demand when the price is $4. The instantaneous rate of change of demand when the price is $4 is boxes per dollar. (Type an integer or a decimal.)Explanation / Answer
A) To find average rate of change
= f (b) -f(a)/(b-a)
= (70-3(4^2)-(70-3 (3^2)/(4-3)
=-48 +27/1
=-21 answer
B) N(p) =70 -3p^2
N' (p) = -6p= -6*3 =-18
C)N(p) =70 -3p^2
N' (p) = -6p= -6*4 =-24