A bakery works out a demand function for its chocolate chip cookies and finds it to be $q=D(x)=711-22 x$, where $q$ is the quantity of cookies sold when the price per cookie, in cents, is $x$. Use this information to answer parts a) through $f$ ).
a) Find the elasticity.
\[
E(x)=
\]

Step 1 ：The price elasticity of demand is a measure of the responsiveness of the quantity demanded to a change in the price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. In this case, the demand function is given by \(D(x) = 711 - 22x\). The elasticity of demand is given by the formula: \(E(x) = x \cdot \frac{D'(x)}{D(x)}\) where \(D'(x)\) is the derivative of the demand function with respect to \(x\).

Step 2 ：First, we need to find the derivative of the demand function. The derivative of \(D(x) = 711 - 22x\) is \(D'(x) = -22\).

Step 3 ：Now that we have the derivative of the demand function, we can substitute it into the formula for the elasticity of demand. Substituting \(D'(x) = -22\) into the formula, we get \(E(x) = x \cdot \frac{-22}{711 - 22x}\).

Step 4 ：Simplifying the above expression, we get \(E(x) = \frac{-22x}{711 - 22x}\).

Step 5 ：\(\boxed{E(x) = \frac{-22x}{711 - 22x}}\) is the final answer for the elasticity of the demand function \(D(x) = 711 - 22x\).