Consider the following demand function with a constant slope. Let $Q(p)$ describe the quantity demanded of the product with respect to price. In this instance $Q(p)$ will take the form $Q(p) = a - b p$ where $0 \le p \le \frac{a}{b}$.
Note: The following is a graph of $p(Q)$ not $Q(p)$.

(Click on graph to enlarge)

The price elasticity of demand as a function of price is given by the equation $E(p) = Q'(p) \frac{p}{Q(p)}$.
Find $\frac{dE}{dp}$ and $\frac{d^2E}{dp^2}$ (your answers should be in terms of $a, b,$ and $p$ ).

$\frac{dE}{dp} =$

$\frac{d^2E}{dp^2} =$

Which of the following graphs best matches the elasticity function for the above demand function?

 A B C D

(Click on a graph to enlarge it.)