(a) Find a function that expresses the number of gallons of gas your car burns on a 420-mile tripin terms of its gas mileage. State the domain of the function. Focus this first part of your letter explaining how to determine this function. Be sure to define the indepedent and dependent variables and include units in the definition. Do not use x and y. Choose meaningful variable names. b) Graph the function from part (a). Does the graph support or refute the claim that at a gas mileage of 28 miles/gallon, the change in the number of gallons required to drive 420 miles is approximately proportional to a small change in the gas mileage? If so, use the graph to determine the sign of the constant of proportionality. What are its units? You should focus this part of your letter on how the proportionality constant is related to the graph.

(c) Use algebra and Definition 1 of the derivative (pg. 141) to confirm your conclusion from part (b) and determine the exact value of the proportionality constant if it exists, or show that there is no such constant. Be sure to follow the templateT1:Derivatives. In particular, do not write a complex fraction (ie. one fraction divided by another. Write a product instead.) No credit given for using Definition 2 of the derivative. d) Write the proportionality relationship. Then use it to approximate how many more (or fewer) gallons your car would burn on a 420-mile trip if its gas mileage were 27.2miles/gallon instead of 28miles/gallon.