The demand, $D$, for a new rollerball pen is given by $D=0.007 p^{3}-0.5 p^{2}+130 p$, where $p$ is the price in dollars. a) Find the rate of change of quantity with respect to price, $d D / d p$. 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 $\mathrm{dD} / \mathrm{dp}$ to be positive or negative? a) $\frac{d D}{d p}=$

Step 1 ：Given the demand function $D=0.007 p^{3}-0.5 p^{2}+130 p$, where $p$ is the price in dollars.

Step 2 ：We are asked to find the rate of change of quantity with respect to price, $\frac{d D}{d p}$.

Step 3 ：We can solve this by applying the power rule for differentiation, which states that the derivative of $x^n$ is $n*x^{n-1}$.

Step 4 ：Applying the power rule to each term in the function, we get $\frac{d D}{d p} = 0.021*p^{2} - 1.0*p + 130$.

Step 5 ：Final Answer: The rate of change of quantity with respect to price, $\frac{d D}{d p}$, is $\boxed{0.021p^{2} - 1.0p + 130}$.