Chapter 8.2, Problem 47E

Land Prices The rectangular region R shown in the following figure represents a city’s financial district. The price of land within the district is approximated by the function

$p(x,y)=200-10{\left(x-\frac{1}{2}\right)}^2-15{\left(y-1\right)}^2$

where p(x, y) is the price of land at the point (x, y) in dollars per square foot and x and y are measured in miles. Compute

$\frac{\partial p}{\partial x}\text{and }\frac{\partial p}{\partial y}(0,1)$

and interpret your results.