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

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

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 dDidp to be positive or negative?

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