Juan works at Texas Burgers in El Paso and earns $8.00 per hour. His twin brother Felipe works in Mexico Burgers in Ciudad Juarez just across the border and earns $3.00 per hour for exactly the same work. An economist looking at this situation sees:

When a company produces and sells x thousand units per week, its total weekly profit is p thousand dollars, where upper p equals startfraction 800 x over 100 plus x squared endfraction . the production level at t weeks from the present is x equals 4 plus 2 t. find the marginal profit, startfraction dp over dx endfraction and the time rate of change of profit, startfraction dp over dt endfraction . how fast (with respect of time) are profits changing when tequals8?