52 CHAPTER 2 Limits and Derivatives 14. The graph (from the US Department of Energy) shows how driving speed affects gas mileage. Fuel economy F is measured in miles per gallon and speed v is measured in miles per hour. (a) What is the meaning of the derivative F'(v)? (b) Sketch the graph of F'(v). (c) At what speed should you drive if you want to save on gas? F (mi/gal) 30 10 10 20 30 40 50 60 70 v(mi/h) 15. The graph shows how the average age of first marriage of Japanese men varied in the last half of the 20th century. Sketch the graph of the derivative function M'(t). During which years was the derivative negative? 20

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