BUS 111 Lecture Notes - Lecture 1: Switch, Pythagorean Theorem
Document Summary
Often, these problems involve many functions of time e. g. revenue increases with number of clients, but clients change over time. This is going to give us mathematically speaking : R(x) with x as a function of time, i. e. x= some formula with t"s in it. In a related rates problem, everything is done implicitly with a whatever/dt on all variables. Example: for jdt landscaping, the revenue from maintaining x homes is given by r(x)=1000x-x2 , and the cost is c(x)=3000 +20x. Write profit function : p(x)= r(x) c(x) P(x)=1000x-x2 (3000+20x) = 980x-x2-3000: dp/dt= 980dx/dt -2xdx/dt, dp/dt= 980(3) -2(400)(3) / month. The profit is increasing by each month. Steps: draw a picture, write equations, etc, differentiate implicitly with respect to time, plug in all known information, write it up. Example: the cost to clean up an oil spill is about / cubic meter per spill for crude oil offshore.
