x$^2+$ xy $-$ y$^2=4$ Find the slope of the tangent line at the point $(2,2).$ Then, find the equation of the tangent line at the point $(2,2).$

Suppose $x=f(p)=150-0\mathrm{.}5p^2$ is the demand function for a certain commodity, where $p$ is the price per pound and $x$ is the quantity demanded in pounds.

$($a$)$ Determine the elasticity of demand function $E(p).$

$($b$)$ Interpret the elasticity of demand at $p=$$$4.$

Provide your answer below:

$($a$)$ The elasticity of demand function is

$($b$)$ The elasticity of demand at the price given is The demand is $.($elastic$/$inelastic$)$