Respuesta :
Answer:
a) -15 unites per dollar
b) -12 units per dollar
c) -18 units per dollar
Step-by-step explanation:
We are given the following in the question:
[tex]N(p) = 100-3p^2, 1\leq p \leq 4[/tex]
where N(p) is the number of boxes of nails at p dollars per box.
a) average rate of change of demand for a change in price from $2 to $3.
Average rate of change =
[tex]\displaystyle\frac{N(3) -N(2)}{3-2}\\\\=\frac{100-3(3)^2-(100 - 3(2)^2)}{1}\\\\= -15\text{ units per dollar}[/tex]
b) instantaneous rate of change of demand when the price is $2
Instantaneous rate =
[tex]N'(p) = \displaystyle\frac{d(N(p))}{dp} = -6p[/tex]
[tex]N'(2) = -6(2) = -12[/tex]
The instantaneous rate of change of demand when the price is $2 is decreasing at 12 units per dollar.
c) instantaneous rate of change of demand when the price is $3
Instantaneous rate =
[tex]N'(3) = -6(8) = -18[/tex]
The instantaneous rate of change of demand when the price is $3 is decreasing at 18 units per dollar.
