Suppose that a rating as a function f budget is given by the function R(B), rating is measured in thumbs up and budget in hundreds of thousands of dollars. R(100)=5 : A movie that costs $10 million to produce will get 5 thumbs up. R-1(4) : The production cost (in $100000) for a movie which got 4 thumbs up. R’(20)=-.5 : A movie which costs $2100000 will be rated APPROXIMATELY .5 thumbs lower than a movie which costs $2000000 to produce. (R-1)’(3)=2 : 2- units are $100000/ thumbs up. 3- units are thumbs up. For a movie that received 3 thumbs up, you would need to increase the production budget by ABOUT $200000 to get 4 thumbs up. P=m(t) is the population of Mexico in millions, where t = number of years since 1980 (dP/dt, t=0 > 0 : In 1980, Mexico’s population was increasing. m-1(97.5)=18 : In 1998 (18 years after 1980) Mexico’s population was 97.5 million people. (m-1)’(97.5)=.46 : When 97.5 million people lived in Mexico, it took ABOUT half a year for the population to increase by another million people. Instantaneous Rate of Change:
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