The demand, $D,$ for a new rollerball pen is given by $D=0\mathrm{.}006p^3-0\mathrm{.}8p^2+180p,$ where $p$ is the price in dollars.

a$)$Find the rate of change of quantity with respect to price, $d\frac{D}{d}p.$

b$)$ How many units will consumers want to buy when the price is $$25$ per unit?

c$)$Find the rate of change at $p=25,$ and interpret this result.

d$)$Would you expect dD$/$dp to be positive or negative?

mpted

a$)\frac{dD}{dp}=$

b$)$ units

$($Round to the nearest integer as needed.$)$

c$)$ The number of consumers who wants to buy will by when the price is $$,$ per unit.

$($Round to the nearest integer as needed.$)$

d$)$ Would vou expect $d\frac{D}{d}p$ to be positive or neqative?