The demand, D $,$ for a new rollerball pen is given by $D=0\mathrm{.}006p^3-0\mathrm{.}8p^{2}120p,$ where p is the price in dollars.

a$)$ Find the rate of change of quantity with respect to price, dDidp.

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

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

d$)$ Would you expect doldp to be positive or negative?