TThe gasoline demand function is: D$($p$)=1200-200$p$.$The elasticity is simplified by considering small changes in $p$ and $D.$ In this case we use the definition of

the derivative and write

$E=\underset{p0}{lim}\frac{\frac{D}{D}}{\frac{p}{p}}=\underset{p0}{lim}\frac{D}{p}(\frac{p}{D})=\frac{dD}{dp}\frac{p}{D}.$

Now the elasticity is a function of $p.$ Show that for the gasoline demand function the elasticity is

$E(p)=-\frac{p}{6-p}.$ The gasoline demand function is: D$($p$)=1200-200$p$.$