Gas mileage actually varies slightly with the driving speed of a car (as well as with highway vs. city driving). Suppose your car averages 28 miles per gallon on the highway if your average
speed Is 51 miles per hour, and it averages 17 miles per gallon on the highway if your average
speed is 68 miles per hour.

a. What is the driving time for a 1700-mile trip if you drive at a speed of 51 miles per
hour? What is the driving time at 68 miles per hour?

b. Assume a gasoline price of $3.39 per gallon. What is the gasoline cost for a 1700 mile
trip if you drive at an average speed of 51 miles per hour? What is the gasoline cost of
68 miles per hour?

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

the answer is a and d