The demand equation for soccer tournament T-shirts is xy − 5,000 = y where y is the number of T-shirts the Enormous State University soccer team can sell at a price of $x per shirt. Find dy dx x = 6 . dy/dx x = 6 = T-shirts per dollar Interpret the result. When the price is set at $6, the demand is by T-shirts per $1 increase in price.

The given equation is: x y – 5000 = y Rewrite this to create an explicit equation: x y – y = 5000 y ( x – 1) = 5000 y = 5000 / (x – 1) Derive to get dy / dx: dy = - 5000 dx / (x – 1)^2 dy / dx = - 5000 / (x – 1)^2   So plugging in x = 6, dy / dx = - 5000 / (6 – 1)^2 dy / dx = - 200