Chapter 4.2, Problem 88E

Driving Costs A study of driving costs based on 2012 medium-sized sedans found that the average cost (car payments, gas, insurance, upkeep, and depreciation) in cents per mile is approximately

$C(x)=\frac{19105}{x^{1.72}}+42.9$ (5 ≤ x ≤ 20)

where x (in thousands) denotes the number of miles the car is driven each year. Show that the graph of C is concave upward on the interval (5, 20). What does your result tell you about the average cost of driving a 2012 medium-sized sedan in terms of the number of miles driven?

Source: American Automobile Association.