The demand, D $,$ for a new rollerball pen is given by $D=0\mathrm{.}006p^3-0\mathrm{.}5p^{2}140p,$ 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?

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